Question

homework | section 3.5 transformation of functions
the university of texas at san antonio
webwork / mat 1023 fall 2025 / sec 3.4 combination and composition
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sec 3.4 combination and comp
(1 point)
suppose (f(x)=x^{3}+8) and (g(x)=sqrt{x}). then
(f(g(x))=)
(g(f(x))=)
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Explanation:

Step1: Find $f(g(x))$

Substitute $g(x)=\sqrt{x}$ into $f(x)$. So $f(g(x))=(\sqrt{x})^{3}+8=x^{\frac{3}{2}} + 8$.

Step2: Find $g(f(x))$

Substitute $f(x)=x^{3}+8$ into $g(x)$. So $g(f(x))=\sqrt{x^{3}+8}$.

Answer:

$f(g(x))=x^{\frac{3}{2}}+8$
$g(f(x))=\sqrt{x^{3}+8}$