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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
`f(x) = cot^(-1)x +x `
`f'(x) = -(1)/(1+x^(2)) +1`
` = (x^(2))/(1+x^(2)),` Clearly, `f'(x) gt 0` for all x
So, f(x) increases in `(-oo,oo)`
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