Explanation
We have the following pair of functions:
[tex]\begin{gathered} f(x)=x^3+6x \\ g(x)=\sqrt{8x} \end{gathered}[/tex]
And we need to find (fog)(2). In order to do this we can start by calculating the composite function (fog)(x)=f(g(x)). Its expression is given by taking the equation of f(x) and replacing x with the expression of g(x). Then we get:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=g(x)^3+6g(x)=(\sqrt{8x})^3+6\sqrt{8x} \\ (f\circ g)(x)=(\sqrt{8x})^3+6\sqrt{8x} \end{gathered}[/tex]
We need to find (fog)(2) so we just need to take x=2 in the equation above:
[tex]\begin{gathered} (f\circ g)(2)=(\sqrt{8\cdot2})^3+6\sqrt{8\cdot2} \\ (f\circ g)(2)=(\sqrt{16})^3+6\cdot\sqrt{16} \\ (f\circ g)(2)=4^3+6\cdot4 \\ (f\circ g)(2)=64+24 \\ (f\circ g)(2)=88 \end{gathered}[/tex]Answer
Then the answer is 88.
