91Ó°ÊÓ

Assume that \(f\) and \(g\) are functions completelv defined bv the followina tables: $$ \begin{array}{r|rr|r} \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{g}(\boldsymbol{x}) \\ \hline 3 & 13 & 3 & 3 \\ 4 & -5 & 8 & \sqrt{7} \\ 6 & \frac{3}{5} & 8.4 & \sqrt{7} \\ 7.3 & -5 & 12.1 & -\frac{2}{7} \end{array} $$ What is the range of \(f ?\)

For Exercises \(1-10,\) evaluate the indicated expression assuming that \(f, g,\) and \(h\) are the functions completely defined by the tables below: $$ \begin{array}{c|cc|c|c|c} \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{g}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{h}(\boldsymbol{x}) \\ \hline \mathbf{1} & \mathbf{4} & \mathbf{1} & 2 & -1 & 3 \\ 2 & 1 & 2 & 4 & 2 & 3 \\ 3 & 2 & 3 & 1 & 3 & 4 \\ 4 & 2 & 4 & 3 & 4 & \mathbf{1} \end{array} $$ $$ (f \circ f)(4) $$

For Exercises \(1-8,\) check your answer by evaluat ing the appropriate function at your answer. $$ \text { Suppose } f(x)=8 x-9 . \text { Find a formula for } f^{-1} $$

Assume that \(f\) and \(g\) are functions completelv defined bv the followina tables: $$ \begin{array}{r|rr|r} \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{g}(\boldsymbol{x}) \\ \hline 3 & 13 & 3 & 3 \\ 4 & -5 & 8 & \sqrt{7} \\ 6 & \frac{3}{5} & 8.4 & \sqrt{7} \\ 7.3 & -5 & 12.1 & -\frac{2}{7} \end{array} $$ What is the range 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 \(g\).

For Exercises \(1-8,\) check your answer by evaluat ing the appropriate function at your answer. $$ \text { Suppose } h(t)=\frac{1+t}{2-t} . \text { Find a formula for } h^{-1} \text {. } $$

Assume that \(f\) and \(g\) are functions completelv defined bv the followina tables: $$ \begin{array}{r|rr|r} \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{g}(\boldsymbol{x}) \\ \hline 3 & 13 & 3 & 3 \\ 4 & -5 & 8 & \sqrt{7} \\ 6 & \frac{3}{5} & 8.4 & \sqrt{7} \\ 7.3 & -5 & 12.1 & -\frac{2}{7} \end{array} $$ Find two different values of \(x\) such that \(f(x)=-5\).

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

For Exercises \(1-10,\) evaluate the indicated expression assuming that \(f, g,\) and \(h\) are the functions completely defined by the tables below: $$ \begin{array}{c|cc|c|c|c} \boldsymbol{x} & \boldsymbol{f}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{g}(\boldsymbol{x}) & \boldsymbol{x} & \boldsymbol{h}(\boldsymbol{x}) \\ \hline \mathbf{1} & \mathbf{4} & \mathbf{1} & 2 & -1 & 3 \\ 2 & 1 & 2 & 4 & 2 & 3 \\ 3 & 2 & 3 & 1 & 3 & 4 \\ 4 & 2 & 4 & 3 & 4 & \mathbf{1} \end{array} $$ $$ (g \circ g)(4) $$

For Exercises \(1-8,\) check your answer by evaluat ing the appropriate function at your answer. $$ \text { Suppose } h(t)=\frac{2-3 t}{4+5 t} . \text { Find a formula for } h^{-1} \text {. } $$