Home
Class 12
MATHS
Let f(x) = e^(x) - x and g (x) = x^(2) -...

Let `f(x) = e^(x) - x` and `g (x) = x^(2) - x, AA x in R`. Then the set of all `x in R` where the function `h(x) = (f o g) (x)` in increasing is : `

A

`[0, 1/2) cap [1, oo)`

B

`[1/2, 0] cap [1, oo)`

C

`[-1, (-1)/(2)] cap [1/2, prop)`

D

`[0, oo)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x) = e^(x)- x and g(x) = x^(2) - x , AA x in R . Then, the set of all x in R , when the function h(x)= (fog)(x) is increasing, is

Let f(x) = 15 -|x-10|, x in R . Then, the set of all values of x, at which the function, g(x) = f(f(x)) is not differentiable, is

Consider f, g and h be three real valued function defined on R. Let f(x)=sin3x+cosx,g(x)=cos3x+sinx and h(x)=f^(2)(x)+g^(2)(x). Then, The length of a longest interval in which the function g=h(x) is increasing, is

Let f(x)=x^(2) and g(X)=sinx for all xepsilonR . Then the set of all x satisfying (f o g o g o f)(x)=(g o g o f)(x) , where (f o g)(x)=f(g(x)) is

Let f(x) = x - x^(2) and g(x) = {x}, AA x in R where denotes fractional part function. Statement I f(g(x)) will be continuous, AA x in R . Statement II f(0) = f(1) and g(x) is periodic with period 1.

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f(x) = 3x + 5 AA x in R, g^(-1)(x) = x^(3) +1 AA x in R , then (f^(-1).g)^(-1)(x) is equal to

Let f''(x) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in