Answer :
To find the value of [tex]\((g \circ h)(-3)\)[/tex], we will follow these steps:
1. Evaluate [tex]\( h(-3) \)[/tex]:
- Given [tex]\( h(x) = 4 - x \)[/tex], substitute [tex]\( x = -3 \)[/tex]:
[tex]\[ h(-3) = 4 - (-3) = 4 + 3 = 7 \][/tex]
2. Evaluate [tex]\( g(h(-3)) \)[/tex]:
- We know [tex]\( h(-3) = 7 \)[/tex]. Now, we need to find [tex]\( g(7) \)[/tex], where the function [tex]\( g(x) \)[/tex] is given by [tex]\( g(x) = \frac{x+1}{x-2} \)[/tex]:
[tex]\[ g(7) = \frac{7 + 1}{7 - 2} = \frac{8}{5} \][/tex]
Thus, the value of [tex]\((g \circ h)(-3)\)[/tex] is [tex]\(\frac{8}{5}\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{\frac{8}{5}} \][/tex]
1. Evaluate [tex]\( h(-3) \)[/tex]:
- Given [tex]\( h(x) = 4 - x \)[/tex], substitute [tex]\( x = -3 \)[/tex]:
[tex]\[ h(-3) = 4 - (-3) = 4 + 3 = 7 \][/tex]
2. Evaluate [tex]\( g(h(-3)) \)[/tex]:
- We know [tex]\( h(-3) = 7 \)[/tex]. Now, we need to find [tex]\( g(7) \)[/tex], where the function [tex]\( g(x) \)[/tex] is given by [tex]\( g(x) = \frac{x+1}{x-2} \)[/tex]:
[tex]\[ g(7) = \frac{7 + 1}{7 - 2} = \frac{8}{5} \][/tex]
Thus, the value of [tex]\((g \circ h)(-3)\)[/tex] is [tex]\(\frac{8}{5}\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{\frac{8}{5}} \][/tex]
