Question

chapter: combining functions consider the following functions Find the formula for (gºf)(x) and simplify your answer. Then find the domain for (gºf)(x). Round your answer to two decimal places, if necessary.

Answer 1

hello

to solve this question, we jusst need to mutilply f(x) and g(x)

$\begin{gathered} f(x)=\frac{x+4}{3} \\ g(x)=\sqrt[]{x+4} \\ (g.f)(x)=\sqrt[]{\frac{x+4}{3}+4} \\ g.f=\sqrt[]{\frac{x+4+12}{3}} \\ g.f=\sqrt[]{\frac{x+16}{3}} \end{gathered}$

to find the domain

solve for x

$\begin{gathered} \frac{x+16}{3}\ge0 \\ x+16\ge0 \\ x\ge-16 \end{gathered}$

domain;

$\begin{gathered} \lbrack R,x\ge-16\rbrack \\ \lbrack-16,\infty\rbrack \end{gathered}$

the domain is all real numbers to x greater than -16