[tex]\boxed{ (f \circ g)(10)=f(g(10))=-18}[/tex]
I think you this exercise is about composition of functions. The definition of composition of functions states:
[tex]The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \ f[/tex]
In this exercise both the function [tex]f[/tex] and [tex]g[/tex] are straight lines, so the domain for both functions is the set of all real numbers, hence [tex]g(x)[/tex] is in fact in the domain of [tex]f[/tex]. So:
[tex](f \circ g)(x)=f(g(x))=-9(x-9)-9 \\ \\ Simplifying: \\ \\ f(g(x))=-9x+81-9 \\ \\ f(g(x))=-9x+72 \\ \\ \\ So \ for \ x=10 \\ \\ (f \circ g)(10): \\ \\ f(g(10))=-9(10)+72 \\ \\ f(g(10))=-90+72 \\ \\ \boxed{ (f \circ g)(10)=f(g(10))=-18 }[/tex]
Transformation of functions: https://brainly.com/question/12469649
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Answer:
The answer is -18 on PLATO.
Step-by-step explanation:
