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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`, when the function `h(x)= (fog)(x)` is increasing, is

A

`[0, infty)`

B

`[-1,-1/2] cup [1/2,infty)`

C

`[0,1/2] cup [1,infty)`

D

`[-1/2,0] cup [1, infty)`

Text Solution

Verified by Experts

The correct Answer is:
C
Here `f(x) =e^(x)-x` and `g(x) =x^(2)-x`
`h'(x) =e^(x^(2)-n)(2x-1)-(2x-1)`
`h'(x) =(2x-1)(e^(x^(2)-x)-1)`

So, `n in [0,1/2] cup [1,infty)`
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