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If [tex]\( g(x) = \frac{x+1}{x-2} \)[/tex] and [tex]\( h(x) = 4 - x \)[/tex], what is the value of [tex]\( (g \circ h)(-3) \)[/tex]?

A. [tex]\( \frac{8}{5} \)[/tex]

B. [tex]\( \frac{5}{2} \)[/tex]

C. [tex]\( \frac{15}{2} \)[/tex]

D. [tex]\( \frac{18}{5} \)[/tex]

Sagot :

GinnyAnswer
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]
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