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:

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

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

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

This is valid for all $x \geq 0$ .

Stumbling Robot