Home
Class 12
MATHS
If f(x)=int(0)^(x)log(0.5)((2t-8)/(t-2))...

If `f(x)=int_(0)^(x)log_(0.5)((2t-8)/(t-2))dt`, then the interval in which f(x) is increasing is (a) `(-oo,2)uu(6,oo)` (b) `(4,6)` (c) `(-oo,2)uu(4,oo)` (d) (2,6)

A

`(-oo,2)uu(6,oo)`

B

`(4,6)`

C

`(-oo,2)uu(4,oo)`

D

(2,6)

Text Solution

Verified by Experts

The correct Answer is:
B
`f'(x)gt0rArrlog_(0.5)((2x-8)/(x-2))gt0`
`rArr" "(2x-8)/(x-2)lt1`
`rArr" "(2x-8)/(x-2)-1lt0`
`rArr" "x in (2,6)`
Also `(2x-8)/(x-2) gt0 rArr" "x lt 0 or x gt 4`
`rArr" "x in (4,6)`
Promotional Banner

Similar Questions

Explore conceptually related problems

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

If (log)_3(x^2-6x+11)lt=1, then the exhaustive range of values of x is: (a) (-oo,2)uu(4,oo) (b) (2,4) (c) (-oo,1)uu(1,3)uu(4,oo) (d) none of these

The domain of f(x)="log"|logx|i s (0,oo) (b) (1,oo) (c) (0,1)uu(1,oo) (d) (-oo,1)

If f(x)=x^2+x+3/4 and g(x)=x^2+a x+1 be two real functions, then the range of a for which g(f(x))=0 has no real solution is (A) (-oo,-2) (B) (-2,2) (C) (-2,oo) (D) (2,oo)

If cos^2x-(c-1)cosx+2cgeq6 for every x in R , then the true set of values of c is (a) (2,oo) (b) (4,oo) (c) (-oo,-2) (d) (-oo,-4)

The domain of the function f(x)=1/(sqrt(|x|-x)) is: (1) (-oo,oo) (2) (0,oo (3) (-oo,""0) (4) (-oo,oo)"-"{0}

The interval in which f(x) defined by f(x) = int_(-1)^x (t^2+2t)(t^2-1) dt increases

If int_(0)^(x)f(t)dt=x^2+int_(x)^(1)t^2f(t)dt , then f((1)/(2)) is equal to

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cot(x/2)sin^2(x/2) does not possess critical points is (a) (-oo,-4/3) (b) (-oo,-1) (c) [1,oo) (d) (2,oo)

Let f: R ->[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the set of values of a for which f is onto is (a) (0,oo) (b) [2,1] (c) [1/4,oo] (d) none of these