Answer:
[tex]f{\circ }g(-8)=\frac{781}{8}[/tex]
Step-by-step explanation:
We have been given two function [tex]f(x)=x^2+7[/tex] and [tex]g(x)=\frac{x-3}{x}[/tex]. We are asked to find [tex]f{\circ }g(-8)[/tex].
By the definition of composite functions [tex]f{\circ}g(x)=f(x)\cdot g(x)[/tex].
[tex]f{\circ }g(-8)=f(-8)\cdot g(-8)[/tex]
[tex]f(-8)=(-8)^2+7[/tex]
[tex]f(-8)=64+7[/tex]
[tex]f(-8)=71[/tex]
[tex]g(-8)=\frac{-8-3}{-8}[/tex]
[tex]g(-8)=\frac{-11}{-8}[/tex]
[tex]g(-8)=\frac{11}{8}[/tex]
[tex]f{\circ }g(-8)=71\cdot \frac{11}{8}[/tex]
[tex]f{\circ }g(-8)=\frac{781}{8}[/tex]
Therefore, [tex]f{\circ}g(x)=\frac{781}{8}[/tex].
