91Ó°ÊÓ

For each of the functions \(f\) given in Exercises \(15-24:\) (a) Find the domain of \(f\). (b) Find the range of \(f\). (c) Find a formula for \(f^{-1}\). (d) Find the domain of \(f^{-1}\). (e) Find the range of \(f^{-1}\). You can check your solutions to part \((c)\) by verifying that \(f^{-1} \circ f=I\) and \(f \circ f^{-1}=I\) (recall that I is the function defined by \(I(x)=x\) ). \(f(x)=2 x-7\)

Evaluate the indicated expression assuming that \(f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1|\). $$ (f \circ g)(3.85) $$

Suppose \(f\) and \(g\) are functions, each with domain 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 \(f ?\)

Evaluate the indicated expression assuming that \(f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1|\). $$ (g \circ f)(0.23) $$

Suppose \(f\) and \(g\) are functions, each with domain 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 \(g\) ?

For each of the functions \(f\) given in Exercises \(15-24:\) (a) Find the domain of \(f\). (b) Find the range of \(f\). (c) Find a formula for \(f^{-1}\). (d) Find the domain of \(f^{-1}\). (e) Find the range of \(f^{-1}\). You can check your solutions to part \((c)\) by verifying that \(f^{-1} \circ f=I\) and \(f \circ f^{-1}=I\) (recall that I is the function defined by \(I(x)=x\) ). \(f(x)=\frac{4}{5 x-3}\)

Suppose \(f\) and \(g\) are functions, each with domain 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 \(f\).

For Exercises 19-26, assume \(f\) is the function defined by $$ f(t)=\left\\{\begin{array}{ll} 2 t+9 & \text { if } t<0 \\ 3 t-10 & \text { if } t \geq 0 \end{array}\right. $$ Evaluate \(f(1)\).

Evaluate the indicated expression assuming that \(f(x)=\sqrt{x}, \quad g(x)=\frac{x+1}{x+2}, \quad h(x)=|x-1|\). $$ (h \circ f)(0.3) $$

For each of the functions \(f\) given in Exercises \(15-24:\) (a) Find the domain of \(f\). (b) Find the range of \(f\). (c) Find a formula for \(f^{-1}\). (d) Find the domain of \(f^{-1}\). (e) Find the range of \(f^{-1}\). You can check your solutions to part \((c)\) by verifying that \(f^{-1} \circ f=I\) and \(f \circ f^{-1}=I\) (recall that I is the function defined by \(I(x)=x\) ). \(f(x)=\frac{2 x}{x+3}\)