Find a formula for the composition of given functions

by RoRi

August 31, 2015

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

$f(x) = \sqrt{x} \quad \text{if } x \geq 0, \qquad g(x) = -x^2.$

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

$\begin{align*} h(x) &= f(g(x)) \\ &= f(-x^2) \\ &= \sqrt{-x^2} \end{align*}$

Since $-x^2 < 0$ if $x \neq 0$ and $f$ is undefined for any $x < 0$ , we have $h(x) = 0$ if $x = 0$ , and $h$ is undefined for all $x \neq 0$ .

Stumbling Robot