Question

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

Options

• R

• (–∞, –1)

• (1, ∞)

• (–1, 1)

Answer 1

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

Explanation:

f(x) = `x/(x^2 + 1)`

`\implies` f'(x) = `((x^2 + 1)(1) - (x)(2x))/(x^2 + 1)^2`

`\implies` f'(x) = `(1 - x^2)/(x^2 + 1)^2`

∵ f(x) is increasing function.

∴ f'(x) > 0

`\implies (1 - x^2)/(x^2 + 1)^2 > 0`

Here x² + 1 ≠ 0, x² ≠ –1

 1 – x² > 0, x² < 1

x ∈ (–1, 1)