Sure, let's break it down step-by-step. We are given [tex]\( h(x) = x - 7 \)[/tex] and [tex]\( g(x) = x^2 \)[/tex].
We need to find the equivalent expression for [tex]\( (g \circ h)(5) \)[/tex].
The notation [tex]\( (g \circ h)(5) \)[/tex] represents the composition of the functions [tex]\( g \)[/tex] and [tex]\( h \)[/tex], applied to the input 5. We perform this in two steps:
1. First, apply the function [tex]\( h(x) \)[/tex] to the input 5:
[tex]\[
h(5) = 5 - 7
\][/tex]
Simplifying this, we obtain:
[tex]\[
h(5) = -2
\][/tex]
2. Next, take the result from the first step and apply the function [tex]\( g(x) \)[/tex] to it:
[tex]\[
g(h(5)) = g(-2)
\][/tex]
Since [tex]\( g(x) = x^2 \)[/tex], we have:
[tex]\[
g(-2) = (-2)^2
\][/tex]
3. Simplify the expression [tex]\( (-2)^2 \)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
So, the value of [tex]\( (g \circ h)(5) \)[/tex] is 4. Therefore, the equivalent expression is:
[tex]\[
(5 - 7)^2
\][/tex]
