If f(x) = -4x + 2 and g(x) = sq root X – 8,what is (fºg)(12)?​

Accepted Solution

Answer:[tex](fog)(12)=-6[/tex]Step-by-step explanation:Recall that the notation: [tex](fog)(12)[/tex] is the same as: [tex]f(g(12))[/tex] which means the value of the function f when you give it as input the value obtained by evaluating g(12).Therefore, we need to start finding what g(12) is using the definition :[tex]g(x)=\sqrt{x-8}[/tex] and evaluating it as x = 12.[tex]g(x)=\sqrt{x-8}\\g(12)=\sqrt{12-8}\\g(12)=\sqrt{4}\\g(12)=2[/tex]So now we use this answer "2" as input for f(x):[tex]f(x)=-4x+2\\f(2)=-4(2)+2\\f(2)=-8+2\\f(2)=-6[/tex]Therefore, [tex](fog)(12)=-6[/tex]