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If [tex]$h(x)=x-7$[/tex] and [tex]$g(x)=x^2$[/tex], which expression is equivalent to [tex]$(g \circ h)(5)$[/tex]?

A. [tex][tex]$(5-7)^2$[/tex][/tex]

B. [tex]$(5)^2-7$[/tex]

C. [tex]$(5)^2(5-7)$[/tex]

D. [tex][tex]$(5-7) x^2$[/tex][/tex]

Sagot :

GinnyAnsweridn
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]
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