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Let [tex]f(x) = x^2 - 20[/tex] and [tex]g(x) = 3 - x[/tex]. Perform the composition or operation indicated.

Find [tex](fg)(-3)[/tex].

[tex](fg)(-3) = \square[/tex]

Sagot :

GinnyAnswer
To find [tex]\((f \circ g)(-3)\)[/tex], we need to first find [tex]\(g(-3)\)[/tex] and then use that result as the input for the function [tex]\(f(x)\)[/tex].

1. Find [tex]\(g(-3)\)[/tex]:

The function [tex]\(g(x)\)[/tex] is given by:
[tex]\[ g(x) = 3 - x \][/tex]
Substituting [tex]\(-3\)[/tex] for [tex]\(x\)[/tex] in [tex]\(g(x)\)[/tex]:
[tex]\[ g(-3) = 3 - (-3) = 3 + 3 = 6 \][/tex]
So, [tex]\(g(-3) = 6\)[/tex].

2. Find [tex]\(f(g(-3))\)[/tex], which is [tex]\(f(6)\)[/tex]:

The function [tex]\(f(x)\)[/tex] is given by:
[tex]\[ f(x) = x^2 - 20 \][/tex]
Substituting [tex]\(6\)[/tex] for [tex]\(x\)[/tex] in [tex]\(f(x)\)[/tex]:
[tex]\[ f(6) = 6^2 - 20 = 36 - 20 = 16 \][/tex]
So, [tex]\(f(6) = 16\)[/tex].

Therefore, the composition [tex]\((f \circ g)(-3)\)[/tex] is:
[tex]\[ (fg)(-3) = 16 \][/tex]

Thus, [tex]\((f g)(-3) = 16\)[/tex].
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