TM
FUNCTION
(DPP -8 )
JEE [MAIN + ADV.] DIVISION
1. Find the range of k for which the equation k ln x – x = 0 posses two distinct solution
(A) (e, ) (B) (0, e) (C) [e, ) (D) cannot be determined
2. The range of the function f(x) = 4 x 2 x 2 1 is
(A) 3, 7 (B) 3, 5 (C) 2, 3 (D) 3, 6
3. If the domain of function g(x) is (0, 1) then the domain of function y = g(2x)+ g (ln|x|) is
(A) (– 1, 0) (B) (– 1, – e/2) (C) (– e, – 1) (D) (– e, 1)
n
4. For x where n I, the range of function
2
f (x) = sgn(sin x) + sgn(cos x) + sgn(tan x) + sgn(cot x) is equal to
[Note : sgn x denotes signum function of x.]
(A) {–2, 4} (B) {–2, 0, 4} (C) {–4, –2, 0, 4} (D) {0, 2, 4}
1
5. Range of the function f(x) = tan 1
[x ] [ x ] 2 | x |
x2
where [] is the greatest integer function.
LM 1 , IJ RS 1 UV g RS 1 , 2UV LM 1 , 2OP
(A)
N4 K (B)
T4 W 2, (C)
T4 W (D)
N4 Q
6. The range of the function f (x ) log
2 7
(4 x 2 x 1) is equal to
cos ec
3
(A) (– , 1] (B) [– 1, ) (C) (– , – 1] (D) [1, )
7. The number of integers belonging to the interval [–3, 30] but not belonging to the range of the
function f(x) = x{x} – x[–x], x R, is
(where [.] and {.} denote the greatest integer function and fractional part respectively)
x
8. Find the range of f x [{.} denotes fractional part functions]
x 1
1 1 1 1
(A) 0, (B) 0, (C) 0, (D) 0,
2 2 2 2
1
9. The range of the function f(x) = x2 + is
X2 1
3
(A) [1, +) (B) [2, +) (C) , (D) None of these
2
10. The domain of f(x) = (3x – 1)P(20 – 4x) will be-
(A) {3,4} (B) {3,4,5} (C) {3,5} (D) {2,3,4,5}
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