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Answered

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Given [tex]\( f(x) = x^2 - 3 \)[/tex] and [tex]\( g(x) = \frac{x+2}{x} \)[/tex], find [tex]\( (g \circ f)(4) \)[/tex].

A. [tex]\( \frac{11}{13} \)[/tex]
B. 6
C. [tex]\( \frac{15}{13} \)[/tex]
D. -6

Sagot :

GinnyAnswer
To find [tex]\( \left(g \circ f\right)(4) \)[/tex], we need to follow these steps:

1. Calculate [tex]\( f(4) \)[/tex]:
Given [tex]\( f(x) = x^2 - 3 \)[/tex],
[tex]\[ f(4) = 4^2 - 3 = 16 - 3 = 13 \][/tex]

2. Calculate [tex]\( g(f(4)) \)[/tex]:
First, substitute [tex]\( f(4) \)[/tex] into the expression for [tex]\( g(x) \)[/tex]. Given [tex]\( g(x) = \frac{x + 2}{x} \)[/tex],
[tex]\[ g(f(4)) = g(13) = \frac{13 + 2}{13} = \frac{15}{13} \][/tex]

Hence, the value of [tex]\( \left(g \circ f\right)(4) \)[/tex] is:
[tex]\[ \frac{15}{13} \][/tex]

Therefore, the correct answer is [tex]\( \frac{15}{13} \)[/tex].
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