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].
