To find the value of [tex]\((g \circ h)(-3)\)[/tex], we need to follow these steps:
1. Evaluate [tex]\(h(-3)\)[/tex]:
Given [tex]\(h(x) = 4 - x\)[/tex],
[tex]\[
h(-3) = 4 - (-3) = 4 + 3 = 7
\][/tex]
2. Substitute [tex]\(h(-3)\)[/tex] into [tex]\(g(x)\)[/tex]:
Since [tex]\(h(-3) = 7\)[/tex], we need to compute [tex]\(g(7)\)[/tex].
3. Evaluate [tex]\(g(7)\)[/tex]:
Given [tex]\(g(x) = \frac{x + 1}{x - 2}\)[/tex],
let’s find [tex]\(g(7)\)[/tex]:
[tex]\[
g(7) = \frac{7 + 1}{7 - 2} = \frac{8}{5}
\][/tex]
Therefore, the value of [tex]\((g \circ h)(-3) = g(h(-3))\)[/tex] is:
[tex]\[
\frac{8}{5}
\][/tex]
So, the correct answer is:
[tex]\(\frac{8}{5}\)[/tex]
