BANSAL CLASSES MATHEMATICS TARGET IIT JEE 2007
QUESTION BANK ON FUNCTIONS AND INVERSE TRIGONOMETRY TRIGONOM ETRY FUNCTIONS FUNCTIO NS
Time Limit : 5 Sitting Each of 60 Minutes Minutes duration approx.
There are 95 questions in this question bank. Only one alternative is correct. Q.1 Let f be a real valued valued function function such that
2002 x
f (x) + 2f
= 3x
for all x > 0. Find f (2). (A) 1000 (B) 2000 Q.2
Soluti Solution on set of the equat equation, ion, cos cos 1 x – sin1 x = cos1(x (A) is a unit set (C) consists of three elements
Q.3
Q.4
Q.5
(C) 3000
(D) 4000 3
)
(B) consists of two elements (D) is a void set
tan 3x 5 1 cos 6x ; g(x) is a function If f (x) 2 ta function having the same time period as that of f(x), then which
of the following can be g(x). (A) (sec23x + cosec23x)tan23x
(B) 2 sin3x + 3cos3x
(C) 2 1 cos2 3x + cosec3x
(D) 3 cosec3x + 2 tan3x
Which one of the following following depicts the graph of an odd function? function?
(A)
(B)
(C)
(D)
The sum of the infini infinite te terms terms of the series series
2 3 2 3 2 3 + cot 1 2 + cot 1 3 + ..... is equal to : 4 4 4
cot 1 1 (A) tan –1 (1) Q.6
(B) tan –1 (2)
(D) tan –1 (4)
Domain Domain of definit definition ion of the functio function n f (x) = log 10·3x 2 9 x 1 1 + cos 1(1 x ) is (A) [0, 1]
Q.7 Q.7
(C) tan –1 (3)
(B) [1, 2]
(C) (0, 2)
(D) (0, 1)
1 tan tan 2A + tan tan 1(cotA)+tan 1(cot3A) for 0 < A < (/4) is 2
The The valu valuee of tan tan1 (A) 4 tan1 (1)
Bansal C lasses
(B) 2 tan1 (2)
(C ) 0
(D) none
QB on Functions & Inverse trigonometry functions
[2]
Q.8
f (x)
Let
g(x) and h(x)
max. sin t : 0 t min. sin t :
x 0 t x
f (x) g(x )
where [ ] denotes greatest integer function, then the range of h(x) is (A) {0, 1} (B) {1, 2} (C) {0, 1, 2} (D) {3, 2, 1, 0, 1, 2, 3} Q.9
(A) 2 Q.10 Q.10
(B) 6
The The valu valuee of
(A) sec Q.11 Q.11
Q.13 Q.13
secsin 1 sin
10
(B) sec
9
31 cos 1 cos 9 9
(D) –1
3x 2 7x 8 denotess the the where [ *] denote 2 1 x (D) ( 2, 5]
(C) [0, 1]
cos sin sin 1 x and = cos 1 sin sin cos cos 1 x , then : = sin 1 cos (A) tan = cot (B) tan = cot (C) tan = tan
8
Give Given n f (x) (x) =
1 x
8 1 x
and
g (x) =
4 f (sin x )
4 f (cos x )
(D) tan = tan
then g(x) is
(B) periodic with period (D) aperiodic
1 1 1 1 + sin1 ; y = cos cos 1 then : 2 2 8 2
If x = tan tan1 1 cos1
(B) y = x
(C) tan x = (4/3 (4/3)) y
(D) (D) tan tan x = (4/3 (4/3)) y
In the square ABCD with side AB = 2 , two points points M & N are on on the adjacent sides of the square such that MN is parallel to the diagonal BD. If x is the distance of MN from the vertex A and f (x) = Area ( AMN) , then range range of f (x) is :
(A) 0 , 2 Q.16
is equal to
(C ) 1
9
The domain domain of definition definition of the function function , f (x) = arc cos
(A) x = y Q.15
is (D) 30
50
(A) periodic with period /2 (C) periodic with period 2 Q.14 Q.14
+ sin
(C) 15
greatest integer function, is : (A) (1, 6) (B) [0, 6) Q.12
x 5
x 3
The period period of the functi function on f(x) f(x) = sin 2 x + sin
(B) (0 , 2 ]
(C ) 0 , 2 2
(D) 0 , 2 3
tan1 tan 8 has the value equal to 7 7
cos cos1 cos
(A) 1
Bansal C lasses
(B) –1
(C) cos
7
(D) 0
QB on Functions & Inverse trigonometry functions
[3]
Q.17
x 5 2
The domain of the definition of the function f(x) = sin 1
1 a 1 a The The valu valuee of tan sin tan sin b b 4 2 4 2 1
(A)
Q.19 Q.19
b
2a
(B)
Q.20
is :
1
1
a
2 b
Let f be be a function satisfying f satisfying f (xy) (xy) = value of f of f (40) (40) is (A) 15
1
(B) ( 7, 3) ( 3, 7) (D) ( 3, 3) (5, 6)
(A) (7, 7) (C) [ 7, 3] [3, 5) (5, 6)
Q.18 Q.18
+ log10 (6 x)
(C)
f ( x ) y
b 2
a
, where (0 < a < b), is
2
(D)
2 b
a
b 2
2
2a
for all positive real numbers x and y. If f If f (30) (30) = 20, then the
(B) 20
(C) 40
(D) 60
Number Number of real value of x satisfy satisfying ing the equation, equation, arctan arc tan xx 1 + arcsin arc sin xx 1 1 = (A) 0
(B) 1
(C ) 2
2
is
(D) more than 2
Q.21 Q.21
Let Let f (x) (x) = sin sin2x + cos 4x + 2 and g (x) = cos (cos x) x) + cos (sin x) also let period of f (x) and g (x) be T1 and T2 respectively then (A) T1 = 2T2 (B) 2T1 = T2 (C) T1 = T2 (D) T1 = 4T2
Q.22
Number Number of solutions solutions of the equation equation 2 cot –12 + cos –1(3/5) = cosec –1 x is (A) 0 (B) 1 (C ) 2 (D) more than 2
Q.23
The domain domain of definition definition of the function function : f (x) = l n ( x2 5 x 24 – x – 2) is (A) (– , –3]
Q.24
(B) (– , –3 ] [8, ) (C)
The period period of the function function f(x) = sin sin cos (A)
(B) 2
2
x
2
, 28 9
(D) none
+ cos(sinx) cos(sinx) equal (C)
(D) 4
Q.25 Q.25
If x = cos cos –1 (cos 4) ; y = sin –1 (sin 3) then which of the following holds ? (A) x – y = 1 (B) x + y + 1 = 0 (C) x + 2y = 2 (D) tan (x + y) = – tan7
Q.26 Q.26
Let Let f (x) (x) = e
{e|x | sgn x}
[ e| x | sgn x ]
and g (x) = e
, x R where { x } and [ ] denotes the fractional part and
integral part functions respectively. Also h (x) = l n f ( x ) + l n g ( x ) then for all real x, h (x) is (A) an odd function (B) an even function (C) neithe neitherr an odd nor nor an even even funct function ion (D) both both odd as well well as even even funct function ion Q.27
–1
The number number of solutions solutions of the equation equation tan (A) 3
Bansal C lasses
(B) 2
x 3
(C ) 1
x = tan –1 x 2
+ tan –1
is
(D) 0
QB on Functions & Inverse trigonometry functions
[4]
Q.28
Which of the the following following is the solution solution set set of the equation equation (A) (0, 1)
Q.29
(B) (–1, 1) – {0}
(C) (–1, 0) 1
Suppos Supposee that that f f is a periodic function with period f (–3) – f 1 4 has the value equal to (A) 2 (B) 3
Q.30 The The valu valuee of tan 1 (A) Q.31
2x 2 1 2 cos cos –1 x = cot –1 2 ? 2 x 1 x
1 2
tan (B)
6
1
(D) [–1, 1] and that f f (2) = 5 and f 9 4 = 2 then
2
(C ) 5
is equal :
52 6 1
(D) 7
6
(C)
4
(D) none
3
Given Given f (x) = (x+1)C(2x– 8) ; g (x) = (2x – 8) C(x + 1) and h (x) = f (x) . g (x) , then which of the following holds ? (A) The domain of 'h' is (B) The The range of 'h' is {– 1} (C) The domain of 'h' is {x / x > 3 or x < – 3 ; x I (D) The range of 'h' is {1}
Q.32 Q.32
Q.33
The The sum sum
n 1
(A) tan1
1
tan 1
+ tan1
2
2 3
4n n
4
2 n2 2
is equal to :
(B) 4 tan 1 1
Range Range of the function function f (x) = tan –1
(C )
[ x]
(D) sec 1
2
[ x]
2 |x|
1 x
2
2
is
where [*] is the greatest integer function. (A)
L 1 , I MN 4 J K
R1 U V T4 W
(B) S
2 , g
(C)
R 1 , 2U S4 V T W
(D)
L 1 , 2O MN 4 PQ
Q.34 Q.3 4
Let [x] denote denote the the greatest greatest integer in x . Then in the interval interval [0, 3] the number number of solutions solutions of of the equation, equation, 2 x 3x + [x] = 0 is : (A) 6 (B) 4 (C ) 2 (D) 0
Q.35
The range range of of values values of p for for which the equation, equation, sin cos –1 cos(tan 1 x) = p has a solution is: (A)
Q.36 Q.36
1 2
Let Let f (x) (x) =
,
2
1
0
(B) [0, 1)
if x is rational and g (x) =
x
if x is irrational
Then the function (f – g) x is (A) odd (C) neither odd nor even
Bansal C lasses
(C )
1 2
, 1
(D) (– 1, 1)
0
if x is irrational
x
if x is rational
(B) even (D) odd as well as even
QB on Functions & Inverse trigonometry functions
[5]
Q.37
5 12 + sin –1 = is x x 2
Number Number of value value of x satisfy satisfying ing the equation equation sin –1 (A) 0
Q.38
(B) 1
(C ) 2
Consider Consider a real valued valued function function f(x) such that
a b is satisfied are 1 ab (A) a (– , 1); b R (C) a (–1, 1) ; b [–1, 1]
(D) more than 2 (x)
1
e
1
e f (x )
= x. The values of 'a' and 'b' for which
f (a) + f (b) = f
Q.39
1 1 The The valu valuee of tan cot (3) equals 2
(A) 3 10 Q.40
Q .4 3
(B) 10 3
1
(B)
(C) 3 10
(D) 10 3
(C) 2
2
The real values values of x satisfy satisfying ing tan –1 x
(A) ± Q.42
1
The period period of the functio function n cos 2 x + cos2x cos 2x is : (A)
Q.41
(B) a (– , 1); b (–1, ) (D) a (–1, 1); b (–1, 1)
1
(B) ±
2
2
x
(D) none of these
4 2 – tan –1 x x x
– tan –1
(C) ± 4 2
2
= 0 are
(D) ± 2
Which of the following is true for a real valued function y = f (x) , defined on [ – a , a]? (A) f (x) can be expressed as a sum or a difference of two even functions (B) f (x) can be expressed as a sum or a difference of two odd functions (C) f (x) can be expressed as a sum or a difference of an odd and an even function (D) f (x) can never be expressed as a sum or a difference of an odd and an even function
1 equals cos 2 tan 1 7 (A) sin (4cot –13)
(B) sin(3cot –14)
(C) cos(3cot –14)
(D) cos(4cot –13)
Q.44
Let Let f(x) f(x) = sin [a ] x (where [ ] denotes denotes the greatest integer function) . If f is periodic periodic with fundamental period , then a belongs to : (A) [2, 3) (B) {4, 5} (C) [4, 5] (D) [4, 5)
Q.45
The range range of of the the function function,, f(x) f(x) = cot cot –1 log 0 .5 x 4
0, 3 (B) 4
(A) (0, ) Q.46
2x 2 3 is:
3 , (C) 4
, 3 (D) 2 4
Which of the following following is the solution set of the equation equation sin –1x = cos –1x + sin –1(3x – 2)? (A)
1 , 1 2
Bansal C lasses
(B)
1 , 1 2
(C)
1 , 1 3
(D)
1 , 1 3
QB on Functions & Inverse trigonometry functions
[6]
Q.47
Which of the the follow following ing functions functions are not not homog homogeneo eneous us ? (A) x + y cos
Q.48
y x
xy xy
2
(C)
(B)
1 , 1 3 3
The functio function n f : R R, defined as f(x) =
(C)
(D)
y sin x y
x y
y y x + l n x x y
l n
1 , 1 3
(D)
1 , 1 2
6 x 10 is : 3x 3 x2
x2
(A) (A) inje inject ctiv ivee but but not not surj surjec ecti tive ve (C) (C) inje inject ctiv ivee as well well as surj surjec ecti tive ve Q.50
x y cos x
Which of the the following following is the solution set of of the equation 3cos –1x = cos –1(4x3 – 3x)? (A) [–1, 1]
Q.49
(B)
(B) (B) surj surjec ecti tive ve but but not not inj injecti ective ve (D) (D) neit neithe herr inje inject ctiv ivee nor nor surj surjec ecti tive ve
The solution solution of the equation equation 2cos 2cos –1x = sin –1 (2x 1 x 2 ) (A) [–1, 0]
(B) [0, 1]
(C) [–1, 1]
(D)
1 2
,1
Q.51
The period period of the function function f f (x) (x) = sin(x + 3 – [x + 3 ] ), where [ ] denotes the greatest integer function is (A) 2 + 3 (B) 2 (C ) 1 (D) 3
Q.52 Q.52
If tan tan –1x + tan –1 2x + tan –13x = , then (A) x = 0 (B) x = 1
Q.53
x2
y2
(B)
4
y2
(C) 4 xy xy
4
(D) none
x 1 2 2
(B) 0,
The range range of the function function y = (A) (– , ) – {± 3} (B) (B)
Q.56
x2
The set of of values values of x for for which which the equation equation cos –1x + cos –1 (A) [0, 1]
Q.55
(D) x
If f(x f(x + ay, ay, x ay) = axy then f(x, y) is equal to : (A)
Q.54
(C) x = –1
1
2
8 9 x2
(C)
8 , 9
I}
(C) R – {n , (2n + 1)
2
3
holds good is
1 ,1 2
(D) {–1, 0, 1}
8 (D) (– , 0) , 9
is (C) 0,
The domain of definition definition of the function function f (x) = (A) R – {n , n
3 3x 2 =
8
9
cot 2 x tan2 x log 1 log 1 2 2 cos ec x 5 3 sec 2 x 5 2 2 (B) R – {(2n + 1) , n I}
is
2
, n I}
(D) none
1 x –1 –1 + cos x = cot x 2
Q.57
The solution solution set of the equation equation sin –1 1 x 2 (A) (A) [–1, [–1, 1] – {0} {0}
Bansal C lasses
(B) (B) (0, (0, 1] U {–1}
(C) [–1, 0) U {1}
– sin –1x
(D) [–1, 1]
QB on Functions & Inverse trigonometry functions
[7]
Q.58
Given the graphs of the two functions, y = f(x) & y = g(x). In the adjacent figure from point A on the graph of the function y = f(x) corresponding to the given value of the independent variable (say x 0), a straight line is drawn parallel to the X-axis to intersect the bisector of the first and the third quadrants at point B . From the t he point B a straight line parallel to the Y-axis is drawn to intersect the graph of the function y = g(x) at C. Again a straight line is drawn from the point C parallel to the X-axis, to intersect the line NN at D . If the straight st raight line NN is parallel parallel to Y-axis, then the co-ord co-ordinates inates of the the point point D are (A) f(x0), g(f(x0)) (B) x0, g(x0) (C) x0, g(f(x0)) (D) f(x0), f(g(x0))
Q.59
The The value value of sin sin –1(sin(2cot –1( 2 – 1))) 1))) is (A) –
4
(B)
4
(C)
3
(D)
4
7 4
Q.60
The functio function n f : [2, ) Y defined by f(x) = x2 4x + 5 is both one-one and onto if : (A) Y = R (B) Y = [1, ) (C) Y = [4, ) (D) [5, )
Q.61
If f(x) f(x) = cosec cosec –1(cosecx) and cosec(cosec –1x) are equal functions then maximum range of values of x is (A) (C)
Q.62 Q.62
1 x 4 5 x2
3
Q.66
(B)
1 x 2
(C)
5x
5 x2
1 x4
(B) 2
(D)
12
(C ) – 2 {x}
1 2
(C) 0,
1
2
x2
3
5 x2
is 3
1 2
(D) 0,
Number of solution(s) solution(s) of the equation cos –1(1 – x) – 2cos –1x = (B) 2
2x 4
where {x} denotes the fractional part function is
1 {x}
(B) 0,
(D) –
Range Range of the function function sgn [ l n (x2 – x + 1) ] is (A) {–1, 0, 1} (B) {–1, 0} (C) – {1}
(A) 3 Q.67 Q.67
Range Range of the function function f (x) =
(A) [0 , 1) Q.65
(B)
Sum of the roots of the equation, equation, arc cot x – arc cot (x + 2) = (A)
Q.64
,0 0 , 2 2 (D) 1, 0 0 ,1
If 2 f(x f(x 2) + 3 f(1/x 2) = x 2 1 (x 0) then f(x2) is : (A)
Q.63
,1 1, 2 2 , 1 1 ,
(C ) 1
(D) {–1, 1}
2
is (D) 0
Let f (x) (x) and g and g (x) (x) be functions which take integers as arguments. Let f (x (x + y) = f = f (x) (x) + g + g (y) (y) + 8 for all integer x integer x and and y y.. Let f (x) (x) = x = x for all negative integers integers x x,, and let g (8) (8) = 17. The value of f (0) (0) is (A) 17 (B) 9 (C) 25 (D) – 17
Bansal C lasses
QB on Functions & Inverse trigonometry functions
[8]
Q.68
–1
There exists a positiv positivee real real numbe numberr x satisfying satisfying cos(tan cos(tan x) = x. The value of cos (A)
Q.69
Q.70 Q.70
(B)
10
2
(C)
5
5
(D)
x 2 is 2
4 5
x 2 2 x 3
The domain domain of the function function,, f(x) = x 0.5log 0.5 x 4 x 2 4 x 3 is : (A)
1 , 2
(C)
1 , 1 3 , 2 2
(B) [1, 3]
cos 7 sin 2 is equal to 5 5 2 23 13
cos cos –1
(A) Q.71 Q.71
–1
(D)
1 , 1 1 , 1 3 , 2 2 2 2
1
(B)
20
20
(C)
33 20
Let f (x) (x) be a function with two properties (a) (a) for any two real real numbe numberr x and y, f (x + y) = x + f (y) and (b) f (0) = 2. The value of f (100), (100), is (A) 2 (B) 98 (C) 102
(D)
17 20
(D) 100
Q.72 Q.72
Let f be a function function such that f that f (3) (3) = 1 and f and f (3x) (3x) = x + f + f (3x (3x – 3) for all x. Then the value of f (300) (300) is (A) 5050 (B) 4950 (C) 5151 (D) none
Q.73 Q.73
If f (x) (x) is an invertible function, and g and g (x) (x) = 2 f 2 f (x) (x) + 5, then the value of g of g –1(x), is (A) 2 f 2 f –1(x) – 5
Q.74 Q.74 Q.75 Q.75
(B)
1
2 f ( x ) 5 1
(C)
1 2
f 1( x ) 5
If f (2x (2x + 1) = 4x2 + 14x, then the sum of the roots of f (x) (x) = 0, is (A) 9/4 (B) 5 (C) – 9/4
(D) f
1 x 5
2
(D) – 5
If y = f (x) (x) is a one-one function and (5, 1) is a point on its graph, which one of the following statements is correct? (A) (1, 5) is a point on the graph of the inverse function y = f –1(x) (B) f (B) f (5) (5) = f (1) (C) the graph of the inverse function y = f = f –1(x) will be symmetric about the y-axis
(D) f f 1 (5) = 1
4 x is x 2 3x 4 (B) [0, ) (D) (– , 1) (1, 4) x
Q.76
Domain Domain of definition definition of the function function f (x) = (A) (– , 0] (C) (– , –1) [0, 4)
Q.77
3
Supp Suppos osee f and g and g are are both linear functions, with f with f (x) (x) = – 2x + 1 and f g ( x) = x. The sum of the slope and the y-intercept of g of g , is (A) – 2 (B) – 1 (C ) 0 (D) 1
Bansal C lasses
QB on Functions & Inverse trigonometry functions
[9]
Q.78
1
(A) 0, Q.79 Q.79
3
(B) 0,
x 5
is
1
1 1 , 6 6 3
(C) (– , 0) (0, ) (D) (D) (0, (0, )
If f (x, (x, y) = max(x , y) min( x , y ) and g and g (x, (x, y) = max(x, y) – min(x, y), then
f g 1,
3 , g (4, 1.75 ) equals 2
(A) – 0.5 Q.80
x 4 3
The range range of the function function f f (x) (x) =
(B) 0.5
(C ) 1
(D) 1.5
The domain domain and and range range of of the the function function f(x) = cosec cosec –1 log3 4 sec x 2 are respectively 1 2 sec x
2
, 2 2
(A) R ;
(C) 2n
2
(B) R + ; 0,
,2n
{ 2n}; 0, 2 2
(D) 2n
2
,2n
{2n}; , {0} 2 2 2
More than one alternatives are correct.
Q.81
The values values of x in in [–2 [–2, 2], for which which the graph graph of the function y = y=–
1 sin x 1 sin x
3 , (B) 2 2
, 2 2
(D) [–2, 2] –
– secx and
, 3 2 2
, 3 2 2
Q.82 Q.82
sin-1(sin3) + sin-1 (sin4) + sin-1(sin5) when simplified reduces to (A) an irrational number (B) a rational number (C) an even prime (D) a negative integer
Q.83
The graphs graphs of of which which of the following following pairs differ differ . (A) y =
1 sin x
+ secx, coincide are
2, 3 3 , 2 (A) 2 2 (C)
1 sin x
sin x 1 tan 2 x
+
cos x 1 cot 2 x
; y = sin 2x
(B) y = tan x cot x ; y = sin x cosec x (C) y = cos x + sin x ; y =
sec x
cos ec x
sec x cos ec x
(D) none of these Q.84
1 2 x + sin 1 2 x , [x] denoting the greatest integer function, then 2 2 1 (A) f (0) = 1 (B) f = (C) f = 0 (D) f() = 0 3 2 3 1
If f(x) f(x) = cos cos
Bansal C lasses
QB on Functions & Inverse trigonometry functions
[10]
Q.85
1 The The value value of cos cos 2 (A) cos
Q.86
7 5
c os
1
14 cos is : 5
(B) sin
2 5
10
(C) cos
The functions functions which are aperiodic aperiodic are : (A) y = [x + 1] (B) y = sin x 2 where [x] denotes greatest greatest integer function
(C) y = sin2 x
(D)
3
cos 5
(D) y = sin1 x
Q .8 7
tan1 x , tan tan1 y, tan1 z are in A.P. A.P. and x , y , z are also in A.P. A.P. (y 0 , 1 , 1) then (A) x , y , z are in G.P. (B) x , y , z are in H.P. (C ) x = y = z (D) (x y)2 + (y z)2 + (z x)2 = 0
Q.88
Which of the the following following function(s) function(s) is/are periodic periodic with with period period . (A) f(x) = sinx (B) f(x) = [x + ] (C) f(x) = cos(sinx) os(sinx) (where [ . ] denotes denotes the greatest integer function)
(D) (D) f(x) f(x) = cos cos2x
Q.89
For the equation equation 2x = tan(2tan tan(2tan –1a) + 2tan(tan –1a + tan –1a3), which of the following is invalid? (A) a2x + 2a = x (B) a2 + 2ax 2ax + 1 = 0 (C) (C) a 0 (D) a –1, 1
Q.90
Which of the functions functions defined defined below are one-one one-one function function(s) (s) ? (A) f(x) f(x) = (x + 1) , ( x 1) (B) g(x) = x + (1 (1/x) ( x > 0) (C) h(x) = x2 + 4x 5, (x > 0) (D) f(x) = e x, ( x 0)
Q.91 Q.91
If cos cos –1x + cos –1y + cos –1z = , then (A) x2 + y2 + z2 + 2xyz = 1 (B) 2(sin –1x + sin –1y + sin –1z) = cos –1x + cos –1y + cos –1z (C) xy + yz + zx = x + y + z – 1
x 1 y 1 z 1 > 6 (D) x + y + z Q.92
Which of the following following homogeneo homogeneous us function functionss are of of degree degree zero ? (A)
Q.93
x y
l n
y y x
+
x
l n
x
–1
The value value of tan
y
(B)
x (x y) y (x y )
x sin 1 x cos
(A) independent of x (C)
2
–
–1
– tan
(C)
xy x
2
y
2
x cos sin
(D) x sin
0, is, for 2 (B) independent of
y x
y cos
x
; x R + , is
(D) none of these
Q .9 4
D [ 1, 1] is the domain of the following functions, state which of them has the inverse. (A) f(x) = x2 (B) g(x) = x3 (C) (C) h(x h(x)) = sin sin 2x (D) (D) k(x k(x)= )= sin sin (x/2)
Q.95 Q.9 5
Which of the following function(s) function(s) have no domain? (A) f(x) = logx – 1(2 – [x] – [x] 2) where [x] denotes the greatest integer function. (B) g(x) = cos –1(2–{x}) where {x} denotes the fractional part function. (C) h(x) = l n l n(cosx) n(cosx) (D) f(x) =
y
1
s e c -1 s g n e x
Bansal C lasses
QB on Functions & Inverse trigonometry functions
[11]
ANSWER KEY , B , A 5 D , C 9 . Q
D , B 4 9 . Q
C , A 3 9 . Q
C , B , A 2 9 . Q
B , 9 . Q A 1
D , C , A 0 9 . Q
C , B 9 8 . Q
D , C , A 8 8 . Q
, C , B , A 7 8 . Q D
D , B , A 6 8 . Q
D , C , B 5 8 . Q
C , B , A 4 8 . Q
C , B , A 3 8 . Q
D , B 2 8 . Q
C , A 1 8 . Q
C 0 8 . Q
D 9 7 . Q
B 8 7 . Q
C 7 7 . Q
C 6 7 . Q
7 . Q A 5
7 . Q D 4
7 . Q D 3
7 . Q A 2
7 . Q C 1
7 . Q D 0
. Q D 9 6
. Q C 8 6
A 7 6 . Q
6 . Q C 6
A 5 6 . Q
C 4 6 . Q
C 3 6 . Q
D 2 6 . Q
A 1 6 . Q
B 0 6 . Q
B 9 5 . Q
C 8 5 . Q
C 7 5 . Q
C 6 5 . Q
5 . Q D 5
C 4 5 . Q
A 3 5 . Q
B 2 5 . Q
5 . Q C 1
5 . Q D 0
4 . Q D 9
4 . Q D 8
C , B 7 4 . Q
4 . Q A 6
C 5 4 . Q
D 4 4 . Q
A 3 4 . Q
C 2 4 . Q
B 1 4 . Q
D 0 4 . Q
A 9 3 . Q
D 8 3 . Q
B 7 3 . Q
A 6 3 . Q
B 5 3 . Q
C 4 3 . Q
C 3 3 . Q
D 2 3 . Q
D 1 3 . Q
3 . Q A 0
2 . Q B 9
2 . Q A 8
2 . Q A 7
2 . Q A 6
2 . Q D 5
2 . Q D 4
2 . Q A 3
2 . Q A 2
2 . Q C 1
C 0 2 . Q
A 9 1 . Q
C 8 1 . Q
C 7 1 . Q
B 6 1 . Q
B 5 1 . Q
C 4 1 . Q
A 3 1 . Q
A 2 1 . Q
A 1 1 . Q
D 0 1 . Q
D 9 . Q
C 8 . Q
A 7 . Q
C 6 . Q
. Q B 5
. Q D 4
. Q A 3
. Q C 2
. Q B 1
Bansal C lasses
QB on Functions & Inverse trigonometry functions
[12]
