Answer:
C
Step-by-step explanation:
Given the two functions, we need to find
(g ° f)(4)
This means, we need to put the function f(x) INTO the function g(x) and then evaluate that new function at x = 4.
We put the whole expression of f(x) into "x" of g(x). Shown below:
[tex]f(x)=x^2-3\\g(x)=\frac{x+2}{x}\\(gof)(x)=\frac{x^2-3+2}{x^2-3}\\(gof)(x)=\frac{x^2-1}{x^2-3}[/tex]
Now we plug in 4 into x and evaluate:
[tex](gof)(x)=\frac{x^2-1}{x^2-3}\\(gof)(4)=\frac{4^2-1}{4^2-3}\\(gof)(4)=\frac{15}{13}[/tex]
Thus,
correct answer is C
