To find the value of [tex]\((g \circ h)(-3)\)[/tex], we need to follow these steps in a detailed manner:
1. Evaluate [tex]\(h(-3)\)[/tex]:
[tex]\[
h(x) = 4 - x
\][/tex]
Substituting [tex]\(x = -3\)[/tex]:
[tex]\[
h(-3) = 4 - (-3) = 4 + 3 = 7
\][/tex]
So, [tex]\(h(-3) = 7\)[/tex].
2. Evaluate [tex]\(g(h(-3))\)[/tex] or [tex]\(g(7)\)[/tex]:
[tex]\[
g(x) = \frac{x + 1}{x - 2}
\][/tex]
Substituting [tex]\(x = 7\)[/tex]:
[tex]\[
g(7) = \frac{7 + 1}{7 - 2} = \frac{8}{5}
\][/tex]
3. Hence, the value of [tex]\((g \circ h)(-3)\)[/tex] is:
[tex]\[
(g \circ h)(-3) = g(h(-3)) = g(7) = \frac{8}{5}
\][/tex]
So, the correct answer is [tex]\(\frac{8}{5}\)[/tex].
