To find the value of [tex]\((g \circ h)(-3)\)[/tex], we need to evaluate [tex]\(g\)[/tex] at the value of [tex]\(h(-3)\)[/tex]. Follow these steps:
1. Evaluate [tex]\(h(-3)\)[/tex]:
The function [tex]\(h(x)\)[/tex] is given by:
[tex]\[
h(x) = 4 - x
\][/tex]
Substitute [tex]\(x = -3\)[/tex] into [tex]\(h(x)\)[/tex]:
[tex]\[
h(-3) = 4 - (-3) = 4 + 3 = 7
\][/tex]
Therefore, [tex]\(h(-3) = 7\)[/tex].
2. Evaluate [tex]\(g(7)\)[/tex]:
The function [tex]\(g(x)\)[/tex] is given by:
[tex]\[
g(x) = \frac{x + 1}{x - 2}
\][/tex]
Substitute [tex]\(x = 7\)[/tex] into [tex]\(g(x)\)[/tex]:
[tex]\[
g(7) = \frac{7 + 1}{7 - 2} = \frac{8}{5} = 1.6
\][/tex]
Therefore, [tex]\(g(7) = 1.6\)[/tex].
So, the value of [tex]\((g \circ h)(-3)\)[/tex] is [tex]\(1.6\)[/tex].
