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Chapter 1: Problem 70
Explain how to determine if two functions are inverses of each other.
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Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}(x-3)^{2}+(y+1)^{2} &=9 \\\y &=x-1\end{aligned}$$
A telephone company offers the following plans. Also given are the piecewise functions that model these plans. Use this information to solve. Plan \(A\) \(\cdot \$ 30\) per month buys 120 minutes. \(\cdot\) Additional time costs \(\$ 0.30\) per minute. $$C(t)=\left\\{\begin{array}{ll}30 & \text { if } 0 \leq t \leq 120 \\\30+0.30(t-120) & \text { if } t>120 \end{array}\right. $$ Plan \(B\) \(\cdot \ 40\) per month buys 200 minutes. \(\cdot\) Additional time costs \(\$ 0.30\) per minute. $$ C(t)=\left\\{\begin{array}{ll} 40 & \text { if } 0 \leq t \leq 200 \\\ 40+0.30(t-200) & \text { if } t>200 \end{array}\right. $$ Simplify the algebraic expression in the second line of the piecewise function for plan B. Then use point-plotting to graph the function.
$$\text { Solve for } y: \quad x=y^{2}-1, y \geq 0$$
Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\frac{1}{2 x}$$
Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}x^{2}+y^{2} &=16 \\\x-y &=4\end{aligned}$$
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