If f(x) = tan–1(g(x)) {where g(x) is monotonically increasin... | MATH - INCREASING AND DECREASING FUNCTION | SolveeIt | Solveeit

Today, August 18

Question

If f(x) = tan^–1(g(x)) {where g(x) is monotonically increasing for 0 < x <p/2} then f(x) is-

A

Increasing in (0, p/2)

B

Decreasing in (0, p/2)

C

Increasing in (0, p/4)

D

Decreasing in (p/4, p/2)

Answer

Increasing in (0, p/2)

Explanation

Solution

f ¢(x) = $\frac{g'(x)}{1 + (g(x))^{2}}$ > 0 " x Î (0, p/2)

{Q g¢(x) > 0 as g(x) is monotonically increasing}