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The function f(x)=cot^(-1)x+x increases ...

The function `f(x)=cot^(-1)x+x` increases in the interval (a) `(1,\ oo)` (b) `(-1,\ oo)` (c) `(-oo,\ oo)` (d) `(0,\ oo)`

A

`(1,oo)`

B

`(-1,oo)`

C

`(-oo,oo)`

D

`(0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `f(x)=cot^(-1)x+x`
`:.f'(x)=-1/(1+x^(2))+1=(x^(2))/(1+x(2))ge0`
Hence `f(x)` in increasing function, since `f'(x)ge0` for all `x`.
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