Answer:
8/5
Step-by-step explanation:
[tex](g\circ h)(-3)[/tex] means [tex]g(h(-3))[/tex].
Start with the inside first: h(-3).
h(-3) means use the function called h and replace the x with -3. The expression that is called h is 4-x.
4-x evaluated at x=-3 gives us 4-(-3)=4+3=7.
So the value for h(-3) is 7, or h(-3)=7.
Now this is what we thus far:
[tex](g\circ h)(-3)=g(h(-3))=g(7)[/tex].
g(7) means use the function called g and replace x with 7. The expression that is called g is (x+1)/(x-2).
(x+1)/(x-2) evaluated at x=7 gives us (7+1)/(7-2)=(8)/(5)=8/5.
This is our final answer:
[tex](g\circ h)(-3)=g(h(-3))=g(7)=\frac{8}{5}[/tex].
