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Find a formula for the composition of given functions

by RoRi

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} \\ &= |x| \end{align*}

This is valid for all x \in \mathbb{R}. (Although f only takes non-negative x, it is not a problem since g(x) \geq 0 for any x \in \mathbb{R}.)

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