To solve for [tex]\((f \circ g)(-2)\)[/tex], we first need to evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = -2\)[/tex], and then use that result to evaluate [tex]\(f(x)\)[/tex].
1. Evaluate [tex]\(g(x)\)[/tex] at [tex]\(x = -2\)[/tex]:
Given [tex]\(g(x) = 5x + 4\)[/tex]:
[tex]\(g(-2) = 5(-2) + 4\)[/tex]
[tex]\(= -10 + 4\)[/tex]
[tex]\(= -6\)[/tex]
2. Evaluate [tex]\(f(x)\)[/tex] at [tex]\(x = g(-2)\)[/tex]:
We found that [tex]\(g(-2) = -6\)[/tex].
Now, use this value in the function [tex]\(f\)[/tex].
Given [tex]\(f(x) = 8 - 10x\)[/tex]:
[tex]\(f(-6) = 8 - 10(-6)\)[/tex]
[tex]\(= 8 + 60\)[/tex]
[tex]\(= 68\)[/tex]
Therefore, the value of [tex]\((f \circ g)(-2)\)[/tex] is [tex]\(68\)[/tex].
