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{:[g(x)=9+(5)/(4)x],[h(x)=10 x-28]:}
Write
(g@h)(x) as an expression in terms of
x.

(g@h)(x)=

$\begin{array}{l} g(x)=9+\frac{5}{4} x \\ h(x)=10 x-28 \end{array}$ $\newline$ Write $(g \circ h)(x)$ as an expression in terms of $x$ . $\newline$ $(g \circ h)(x)=$

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Compare linear and exponential growth

Full solution

Q.

\begin{array}{l} g(x)=9+\frac{5}{4} x \\ h(x)=10 x-28 \end{array}

\newline

Write

(g \circ h)(x)

as an expression in terms of

x

.

\newline

(g \circ h)(x)=

Substitute Functions: To find the composition of functions $(g \circ h)(x)$ , we need to substitute the function $h(x)$ into the function $g(x)$ . This means we will replace every instance of $x$ in $g(x)$ with the expression that defines $h(x)$ .
Write Functions: First, let's write down the functions $g(x)$ and $h(x)$ for clarity: $\newline$ $g(x) = 9 + \frac{5}{4}x$ $\newline$ $h(x) = 10x - 28$ $\newline$ Now, we will substitute $h(x)$ into $g(x)$ .
Distribute and Simplify: Substitute $h(x)$ into $g(x)$ :
$(g@h)(x) = g(h(x)) = 9 + \left(\frac{5}{4}\right)(h(x))$
Now, replace $h(x)$ with its expression:
$(g@h)(x) = 9 + \left(\frac{5}{4}\right)(10x - 28)$
Combine Terms: Next, distribute the $(5/4)$ across the terms in the parentheses: $(g@h)(x) = 9 + \frac{5}{4}\cdot 10x - \frac{5}{4}\cdot 28$
Combine Terms: Next, distribute the $(5/4)$ across the terms in the parentheses: $\newline$ $(g@h)(x) = 9 + (5/4)\cdot 10x - (5/4)\cdot 28$ Simplify the expression by multiplying the constants: $\newline$ $(g@h)(x) = 9 + (50/4)x - (140/4)$ $\newline$ $(g@h)(x) = 9 + (50/4)x - 35$
Combine Terms: Next, distribute the $(5/4)$ across the terms in the parentheses: $\newline$ $(g@h)(x) = 9 + (5/4)\cdot 10x - (5/4)\cdot 28$ Simplify the expression by multiplying the constants: $\newline$ $(g@h)(x) = 9 + (50/4)x - (140/4)$ $\newline$ $(g@h)(x) = 9 + (50/4)x - 35$ Combine the constant terms: $\newline$ $(g@h)(x) = 9 - 35 + (50/4)x$ $\newline$ $(g@h)(x) = -26 + (50/4)x$

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