91Ó°ÊÓ

Find the domain of each function $$ f(x)=\frac{\sqrt{x+4}}{x-4} $$

Tables of values for \(f(x), g(x),\) and \(h(x)\) are given below. Write \(g(x)\) and \(h(x)\) as transformations of \(f(x)\). $$ \begin{aligned} &\begin{array}{|c|c|} \hline x & f(x) \\ \hline-2 & -2 \\ \hline-1 & -1 \\ \hline 0 & -3 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline x & g(x) \\ \hline-1 & -2 \\ \hline 0 & -1 \\ \hline 1 & -3 \\ \hline 2 & 1 \\ \hline 3 & 2 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline x & h(x) \\ \hline-2 & -1 \\ \hline-1 & 0 \\ \hline 0 & -2 \\ \hline 1 & 2 \\ \hline 2 & 3 \\ \hline \end{array} \end{aligned} $$

For each function below, find \(f^{-1}(x)\) $$ f(x)=2-x $$

Tables of values for \(f(x), g(x),\) and \(h(x)\) are given below. Write \(g(x)\) and \(h(x)\) as transformations of \(f(x)\). $$ \begin{aligned} &\begin{array}{|c|c|} \hline x & f(x) \\ \hline-2 & -1 \\ \hline-1 & -3 \\ \hline 0 & 4 \\ \hline 1 & 2 \\ \hline 2 & 1 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline x & g(x) \\ \hline-3 & -1 \\ \hline-2 & -3 \\ \hline-1 & 4 \\ \hline 0 & 2 \\ \hline 1 & 1 \\ \hline \end{array}\\\ &\begin{array}{|c|c|} \hline x & h(x) \\ \hline-2 & -2 \\ \hline-1 & -4 \\ \hline 0 & 3 \\ \hline 1 & 1 \\ \hline 2 & 0 \\ \hline \end{array} \end{aligned} $$

Find the domain of each function $$ f(x)=\frac{\sqrt{x+5}}{x-6} $$

Find the average rate of change of each function on the interval specified. Your answers will be expressions involving a parameter \((b\) or \(h)\). \(b(x)=\frac{1}{x+3}\) on \([1,1+h]\)

For each function below, find \(f^{-1}(x)\) $$ f(x)=3-x $$

Find the average rate of change of each function on the interval specified. Your answers will be expressions involving a parameter \((b\) or \(h)\). \(j(x)=3 x^{3}\) on \([1,1+h]\)

For each function below, find \(f^{-1}(x)\) $$ f(x)=11 x+7 $$

Find the domain of each function $$ f(x)=\frac{x-8}{x^{2}+8 x-9} $$