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Chapter 0: Problem 35
Solve the equation and check your solution. (If not possible, explain why.) $$ 3=2+\frac{2}{z+2} $$
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Average Cost The inventor of a new game believes that the variable cost for producing the game is \(\$ 0.95\) per unit and the fixed costs are \(\$ 6000\). The inventor sells each game for \(\$ 1.69\). Let \(x\) be the number of games sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost \(C\) as a function of the number of games sold. (b) Write the average cost per unit \(\bar{C}=C / x\) as a function of \(x\).
You need a total of 50 pounds of two types of ground beef costing \(\$ 1.25\) and \(\$ 1.60\) per pound, respectively. A model for the total cost \(y\) of the two types of beef is $$ y=1.25 x+1.60(50-x) $$ where \(x\) is the number of pounds of the less expensive ground beef. (a) Find the inverse function of the cost function. What does each variable represent in the inverse function? (b) Use the context of the problem to determine the domain of the inverse function. (c) Determine the number of pounds of the less expensive ground beef purchased when the total cost is \(\$ 73\).
Find the average rate of change of the function from \(x_{1}\) to \(x_{2}\). $$ \begin{array}{cc} \text { Function } & x \text {-Values } \\ f(x)=-\sqrt{x+1}+3 &\quad x_{1}=3, x_{2}=8 \end{array} $$
In Exercises 55-68, determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{2 x+3} $$
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 \(f^{-1}\). $$ f(x)=\sqrt{4-x^{2}}, \quad 0 \leq x \leq 2 $$
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