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The function f(x)=log(1+x)(2x)/(2+x) is ...

The function `f(x)=log(1+x)_(2x)/(2+x)` is increasing on

A

`(0,oo)`

B

`(-oo,0)`

C

`(-oo,oo)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`"Given "f(x)=log(1+x)-(2x)/(2+x)`
`therefore f'(x)=(1)/(1+x)-((2+x).2-2x)/((2+x)^(2))`
`=(x^(2))/((1+x)(x+2)^(2))`
Clearly, `f(x) gt 0` for all `x gt 0`
Hence, rf(x) is increasing on `(0,oo)`
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