Answer:
[tex]g(h(-3)) = \frac{8}{5}[/tex]
Step-by-step explanation:
Given:
[tex]g(x)=\frac{x+1}{x-2} \\[/tex]
[tex]h(x)=4-x[/tex]
Find [tex]g(h(-3))[/tex]
What this problem is asking is find the value of [tex]h(-3)[/tex] and then put that answer into [tex]g(x).[/tex]
Let's find [tex]h(-3)[/tex].
[tex]h(x)=4-x\\h(-3)=4-(-3)\\h(-3)=7[/tex]
Now that we found that [tex]h(-3)[/tex] is equal to 7, we put the value of 7 into [tex]g(x).[/tex]
[tex]g(x)=\frac{x+1}{x-2}\\g(7)=\frac{7+1}{7-2} \\g(7)=\frac{8}{5}[/tex]
Our final answer is
[tex]g(h(-3)) = \frac{8}{5}[/tex]
