Answer :
Answer: 4
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Work Shown:
[tex](g \circ h)(x) = g(h(x))[/tex]
[tex]g(x) = x^2\\\\g(h(x)) = (h(x))^2 \ \text{replace every x with h(x)}\\\\g(h(x)) = (x-7)^2 \ \text{replace h(x) with x-7}\\\\(g \circ h)(x) = (x-7)^2[/tex]
Now plug in x = 5
[tex](g \circ h)(x) = (x-7)^2 \\\\(g \circ h)(5) = (5-7)^2 \\\\(g \circ h)(5) = (-2)^2\\\\ (g \circ h)(5) = 4[/tex]
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Alternative approach:
h(x) = x-7
h(5) = 5-7
h(5) = -2
So this means
g(h(5)) = g(-2)
and
g(x) = x^2
g(-2) = (-2)^2
g(-2) = 4
Therefore making
[tex]g(-2) = g(h(5)) = (g \circ h)(5) = 4[/tex]