Kyle Thomas If $$ h(x)=(x-5)^{2} $$, find functions $$ f(x) $$ and $$ g(x) $$ so that $$ h(x)=f(g(x)) $$, $$ f(x)= $$

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$$ f(x) = x^2 $$ $$ g(x) = x - 5 $$ To express the function $$ h(x) = (x - 5)^2 $$ in the form $$ h(x) = f(g(x)) $$, we need to choose appropriate functions $$ f(x) $$ and $$ g(x) $$. A common approach is to let $$ g(x) $$ be the inner function that transforms $$ x $$ into something that can be squared, and then let $$ f(x) $$ be the outer function that squares its input. Let's choose: 1. $$ g(x) = x - 5 $$ (this will shift $$ x $$ by 5) 2. $$ f(x) = x^2 $$ (this will square the result from $$ g(x) $$) Now, we can check if this works: $$ h(x) = f(g(x)) = f(x - 5) = (x - 5)^2 $$ Thus, we have: - $$ f(x) = x^2 $$ - $$ g(x) = x - 5 $$ So, the functions are: $$ f(x) = x^2 $$ $$ g(x) = x - 5 $$

Kyle Thomas If \( h(x)=(x-5)^{2} \), find functions \( f(x) \) and \( g(x) \) so that \( h(x)=f(g(x)) \), \( f(x)= \)

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Kyle Thomas If \( h(x)=(x-5)^{2} \), find functions \( f(x) \) and \( g(x) \) so that \( h(x)=f(g(x)) \), \( f(x)= \)

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