91Ó°ÊÓ

In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{x-3}{x+2} $$

In Exercises 39-54, (a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{6 x+4}{4 x+5} $$

Communications The cost of using a telephone calling card is \(\$ 1.05\) for the first minute and \(\$ 0.38\) for each additional minute or portion of a minute. (a) A customer needs a model for the cost \(C\) of using a calling card for a call lasting \(t\) minutes. Which of the following is the appropriate model? Explain. $$ \begin{aligned} &C_{1}(t)=1.05+0.38 \llbracket t-1 \rrbracket \\ &C_{2}(t)=1.05-0.38 \llbracket-(t-1) \rrbracket \end{aligned} $$ (b) Graph the appropriate model. Determine the cost of a call lasting 18 minutes and 45 seconds.

Physics A pebble is dropped into a calm pond, causing ripples in the form of concentric circles (see figure). The radius \(r\) (in feet) of the outer ripple is \(r(t)=0.6 t\), where \(t\) is the time in seconds after the pebble strikes the water. The area \(A\) of the circle is given by the function \(A(r)=\pi r^{2}\). Find and interpret \((A \circ r)(t)\).

The distance between \(x\) and \(-10\) is at least 6 .

Consumer Awareness The suggested retail price of a new hybrid car is \(p\) dollars. The dealership advertises a factory rebate of \(\$ 2000\) and a \(10 \%\) discount. (a) Write a function \(R\) in terms of \(p\) giving the cost of the hybrid car after receiving the rebate from the factory. (b) Write a function \(S\) in terms of \(p\) giving the cost of the hybrid car after receiving the dealership discount. (c) Form the composite functions \((R \circ S)(p)\) and \((S \circ R)(p)\) and interpret each. (d) Find \((R \circ S)(20,500)\) and \((S \circ R)(20,500)\). Which yields the lower cost for the hybrid car? Explain.

Write the slope-intercept forms of the equations of the lines through the given point (a) parallel to the given line and (b) perpendicular to the given line. \((2,1)\) Line $$ \begin{aligned} &4 x-2 y=3 \\ &x+y=7 \\ &3 x+4 y=7 \\ &5 x+3 y=0 \\ &y=-3 \\ &y=1 \\ &x=4 \\ &x=-2 \\ &x-y=4 \\ &6 x+2 y=9 \end{aligned} $$

\(y\) is at least six units from 0 .

Determine whether the statement is true or false. Justify your answer. If the graph of the parent function \(f(x)=x^{2}\) is moved six units to the right, three units upward, and reflected in the \(x\)-axis, then the point \((-2,19)\) will lie on the graph of the transformation.

Solve the equation by extracting square roots. $$ x^{2}=11 $$