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If a function f(x) increases in the inte...

If a function `f(x)` increases in the interval `(a, b).` then the function `phi(x) = [f(x)]^n` increases in the same interval and `phi(x) != f(x)` if

A

`n=-1`

B

n=0

C

n=3

D

n=4

Text Solution

Verified by Experts

The correct Answer is:
C
`phi(x ) =[f(x)]^(n) rArr phi. (x) =n[f(x)^(n-1) f.(x)`
as f(x) is increasing function in (a, b) hence `f.(0) gt 0, AA x in (a, b)`
if `phi f(x)` is increasing function then
`n-1=2, n=3`
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