Find a formula for the composition of given functions

by RoRi

September 1, 2015

Find the composition function $h(x) = (f \circ g)(x) = f(g(x))$ of the functions:

$f(x) = \sqrt{x}, \qquad \text{if } x \geq 0, \qquad g(x) = \sin x.$

We compute $h(x) = f(g(x))$ ,

$\begin{align*} h(x) &= f(g(x)) \\ &= f(\sin x) \\ &= \sqrt{\sin x} \end{align*}$

This is valid for all $2n \pi \leq x \leq (2n+1) \pi$ where $n \in \mathbb{Z}$ . (These are the values for which $\sin x \geq 0$ .)

Stumbling Robot