Answer:
[tex]\[\frac{171}{13}\][/tex]
Step-by-step explanation:
Given functions f(x) and g(x) are:
[tex]f(x)=\[x^{2}-3\][/tex]
[tex]g(x)=\[x+\frac{2}{x}\][/tex]
Then, (g o f)(x)=g(f(x))=g([tex]\[x^{2}-3\][/tex])
[tex]=\[x^{2}-3+\frac{2}{x^{2}-3}\][/tex]
[tex]=\[x^{2}-3+\frac{2}{x^{2}-3}\][/tex]
Evaluating the value of (g o f)(x) when x=4,
[tex]=\[4^{2}-3+\frac{2}{4^{2}-3}\][/tex]
[tex]=\[16-3+\frac{2}{16-3}\][/tex]
[tex]=\[13+\frac{2}{13}\][/tex]
[tex]=\[\frac{171}{13}\][/tex]
