The function f(x) = x/1 + |x| is A. strictly increasing B. strictly decreasing

Question

The function f(x) = \(\frac{\text{x}}{1 + |\text{x}|}\) is

A. Strictly increasing

B. Strictly decreasing

C. Neither increasing nor decreasing

D. None of these

Answer 1

Correct answer is A.

Formula:-

(i) The necessary and sufficient condition for differentiable function defined on (a, b) to be strictly increasing on (a, b) is that f’(x) > 0 for all x ∈ (a, b)

Both are increasing for f’(x) > 0