Question

The function f(x) = |[(e^2x – 1)/(e^2x + 1)]| is

(a) Increasing 

(b) Decreasing 

(c) Even 

(d) Strictly increasing

Answer 1

The correct option (a) Increasing

Explanation:

f(x) = [(e^2x – 1)/(e^2x + 1)]

∴ f'(x) = [{[(e^2x + 1) (e^2x) – (e^2x – 1)(e^2x)]²}/{(e^2x + 1)²}]

= [{[e^2x + e^2x – e^4x + e^2x] × 2}/{(1 + e^2x)²}] = [{4e^2x}/{(1 + e^2x)²}]

f'(x) = [{4e^2x}/{(1 + e^2x)²}] > 0

 ⇒ f(x) is increasing function.