91Ó°ÊÓ

Suppose \(f\) and \(g\) are functions, each of whose domain consists of four numbers, with \(f\) and \(g\) defined by the tables below: $$ \begin{array}{c|c} {x} & {f}({x}) \\ \hline {1} & 4 \\ 2 & 5 \\ 3 & 2 \\ 4 & 3 \end{array} $$ $$ \begin{array}{c|c} x & g(x) \\ \hline 2 & 3 \\ 3 & 2 \\ 4 & 4 \\ 5 & 1 \end{array} $$ What is the range of \(g^{-1} ?\)

For Exercises 11-24, evaluate the indicated expression assuming that $$ f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1| $$ $$ (f \circ g)(5) $$

Find all functions (displayed as tables) whose domain is \(\\{-1,0, \pi\\}\) and whose range is \(\\{-3, \sqrt{2}, 5\\}\).

For Exercises 11-24, evaluate the indicated expression assuming that $$ f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1| $$ $$ (g \circ f)(4) $$

Find all functions (displayed as tables) whose domain is {3,5,9} and whose range is {2,4} .

Suppose \(f\) and \(g\) are functions, each of whose domain consists of four numbers, with \(f\) and \(g\) defined by the tables below: $$ \begin{array}{c|c} {x} & {f}({x}) \\ \hline {1} & 4 \\ 2 & 5 \\ 3 & 2 \\ 4 & 3 \end{array} $$ $$ \begin{array}{c|c} x & g(x) \\ \hline 2 & 3 \\ 3 & 2 \\ 4 & 4 \\ 5 & 1 \end{array} $$ Sketch the graph of \(f^{-1}\).

Assume that \(g\) and \(h\) are the functions completely defined by the tables below: $$ \begin{array}{r|r} \boldsymbol{x} & \boldsymbol{g}(\boldsymbol{x}) \\ \hline-3 & -\mathbf{1} \\ -\mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{2} .5 \\ \mathbf{3} & -2 \end{array} $$ $$ \begin{array}{r|r} \boldsymbol{x} & \boldsymbol{h}(\boldsymbol{x}) \\ \hline-4 & 2 \\ -2 & -3 \\ 2 & -1.5 \\ 3 & 1 \end{array} $$ What is the domain of \(g\) ?

Suppose \(f\) and \(g\) are functions, each of whose domain consists of four numbers, with \(f\) and \(g\) defined by the tables below: $$ \begin{array}{c|c} {x} & {f}({x}) \\ \hline {1} & 4 \\ 2 & 5 \\ 3 & 2 \\ 4 & 3 \end{array} $$ $$ \begin{array}{c|c} x & g(x) \\ \hline 2 & 3 \\ 3 & 2 \\ 4 & 4 \\ 5 & 1 \end{array} $$ Sketch the graph of \(g^{-1}\).

For Exercises 11-24, evaluate the indicated expression assuming that $$ f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1| $$ $$ (g \circ f)(5) $$

Find all functions (displayed as tables) whose domain is {0,2,8} and whose range is {6,9} .