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${:[f(x)=x^(3)-6],[h(x)=root(3)(2x-15)]:} Write f(h(x)) as an expression in terms of x. f(h(x))= ◻$

$\begin{array}{l} f(x)=x^{3}-6 \\ h(x)=\sqrt[3]{2 x-15} \end{array}$ $\newline$ Write $f(h(x))$ as an expression in terms of $x$ . $\newline$ $f(h(x))=$ $\newline$ $\square$

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Evaluate an exponential function

Full solution

Q.

\begin{array}{l} f(x)=x^{3}-6 \\ h(x)=\sqrt[3]{2 x-15} \end{array}

\newline

Write

f(h(x))

as an expression in terms of

x

.

\newline

f(h(x))=

\newline

\square

Plug in $h(x)$ : $f(h(x)) = (h(x))^3 - 6$ $\newline$ Now we plug in the expression for $h(x)$ which is the cube root of $(2x - 15)$ .
Simplify cube root: $f(h(x)) = (\sqrt[3]{2x - 15})^3 - 6$ $\newline$ We simplify the cube of the cube root, which cancels out to just $2x - 15$ .
Combine like terms: $f(h(x)) = (2x - 15) - 6$ $\newline$ Now we combine like terms.
Final simplification: $f(h(x)) = 2x - 15 - 6$ $\newline$ $f(h(x)) = 2x - 21$ $\newline$ We have simplified the expression for $f(h(x))$ .

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