Answer: B.4
Explanation:
We have the following fucntions:
[tex]\begin{gathered} f(x)=x-2 \\ g(x)=x^2 \end{gathered}[/tex]We need to find the composition:
[tex](g\circ f)(4)[/tex]For this, first we need to find:
[tex](g\circ f)(x)[/tex]Which by the definition of composition of functions is:
[tex](g\circ f)(x)=g(f(x))[/tex]So we need to substitute f(x), in the x of g(x), as follows:
[tex](g\circ f)(x)=g(f(x))=(x-2)^2[/tex]This is because of how f(x) and g(x) are defined in the problem.
Now, we find what we are asked for:
[tex](g\circ f)(4)[/tex]we are going to need to substitute the value of x=4 into what we found for (gof)(x):
[tex]\begin{gathered} (g\circ f)(4)=(4-2)^2 \\ (g\circ f)(4)=(2)^2 \\ (g\circ f)(4)=4 \end{gathered}[/tex]The answer is B.4
