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Find the range of tan^(-1)((2x)/(1+x^2))...

Find the range of `tan^(-1)((2x)/(1+x^2))`

A

`[-(pi)/(4), (pi)/(4)]`

B

`(-(pi)/(2), (pi)/(2))`

C

`(-(pi)/(2), (pi)/(4)]`

D

`[(pi)/(4), (pi)/(2)]`

Text Solution

Verified by Experts

The correct Answer is:
A
`1 + x^(2) ge 2 |x|`
or `(2|x|)/(1 + x^(2)) le 1`
or `-1 le (2x)/(1 + x^(2)) le 1`
`rArr tan^(-1) ((2x)/(1 + x^(2))) in [-(pi)/(4), (pi)/(4)]`
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