Answer:
28
Step-by-step explanation:
Given: [tex]$ g(x) = x^2 + 3 $[/tex] and [tex]$ h(x) = x - 2 $[/tex].
To find the composition of the functions: [tex]$ (g \circ h)(x) = g(h(x)) $[/tex]
Here, [tex]$ g(h(x)) = g(x - 2) $[/tex]
[tex]$ \implies (x - 2)^2 + 3 $[/tex]
[tex]$ \implies x^2 -4x + 4 + 3 = x^2 - 4x +7 $[/tex]
We are to find [tex]$ g(h(7)) $[/tex]. That is to substitute [tex]$ 7 $[/tex] in the place of [tex]$ x $[/tex].
We get: [tex]$ (7)^2 -4(7) + 7 = 49 - 28 + 7 = 28 $[/tex]
