Question

Please help w/ composition of functions. I did 3√14-(-11) -8 and got 7 as my answer and would appreciate verification that it's correct.

Answer 1

SOLUTION

We were given

$\begin{gathered} f(c)=3c-8\text{ and } \\ g(c)=\sqrt[]{14-c} \\ We\text{ want to find } \\ (fog)(-11) \end{gathered}$

First we will find

$\begin{gathered} f(g(c)\text{ we have } \\ f(g(c)=3(\sqrt[]{14-c})-8 \end{gathered}$

Now

$\begin{gathered} (fog)(-11)\text{ becomes } \\ (fog)=3(\sqrt[]{14-c})-8 \\ (fog)(-11)=3(\sqrt[]{14-(-11})-8 \\ =3\sqrt[]{14+11}-8 \\ =3\sqrt[]{25}-8 \\ (3\times5)-8 \\ =15-8 \\ =7 \end{gathered}$

Hence, the answer is 7