To solve [tex]$(g \circ h)(5)$[/tex], we need to understand that this represents the composition of the functions [tex]\( g \)[/tex] and [tex]\( h \)[/tex] evaluated at [tex]\( x = 5 \)[/tex].
First, we need to find [tex]\( h(5) \)[/tex]:
[tex]\[ h(x) = x - 7 \][/tex]
So,
[tex]\[ h(5) = 5 - 7 \][/tex]
[tex]\[ h(5) = -2 \][/tex]
Next, we take the result of [tex]\( h(5) \)[/tex] and use it as the input for the function [tex]\( g \)[/tex]:
[tex]\[ g(x) = x^2 \][/tex]
So,
[tex]\[ g(h(5)) = g(-2) \][/tex]
[tex]\[ g(-2) = (-2)^2 \][/tex]
[tex]\[ g(-2) = 4 \][/tex]
Therefore, the expression equivalent to [tex]\( (g \circ h)(5) \)[/tex] is [tex]\((5-7)^2\)[/tex].
Thus, the correct answer is:
[tex]\[ (5-7)^2 \][/tex]
