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)`
`implies 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 increasinig function,
`thereforef'(x) gt0`
`implies(1-x^(2))/((x^(2)+1)^(2))gt0`
`implies1-x^(2)gt0`
`impliesx^(2)lt1`
`implies-1ltxlt1`
`implies x in (-1,1)`
Hence, option d is correct.