If `f(x)=(x)/(x^(2)+1)` is increasing function, then the value of x lies in

Options

A. R
B. `(-oo,-1)`
C. `(1,oo)`
D. `(-1,1)`

Answer

D

Explanation

Given , `f(x)= (x)/(x^(2)+1)`
`rArr f'(x)=((x^(2)+1)xx1-x(2x))/((x^(2)+1)^(2))`
`=((x^(2)+1-2x^(2)))/((x^(2)+1)^(2))=(1-x^(2))/((x^(2)+1)^(2))`
Since, `f(x)` is increasing function.
`:.f'(x) gt 0`
`rArr (1-x^(2))/((x^(2)+1)^(2)) gt 0`
`rArr 1-x^(2) gt0`
`rArr x^(2) lt 1`
`rArr-1 lt x lt 1`
`x in ( -1, 1)`
Hence, option (d) is correct.