Chapter 4.7, Problem 7CYU

a.

To determine

To find: The inverse of the function $C(x)$ .

Answer to Problem 7CYU

  $C^{-1}(x)=\frac{x-600}{70}$

Explanation of Solution

Given information: The function of total monthly cost is $C(x)=600+70x$

Calculation:

Let the $C(x)$ as y then we can rewrite the function as $y=600+70x$

Now, swap the variables to find inverse

  $x=600+70y$

Solve it for y to get inverse function.

Subtract both sides 600.

  $x-600=70y$

Divide both sides by 70.

  $\frac{x-600}{70}=\frac{70y}{70}$

Simplify it,

  $y=\frac{x-600}{70}$

So, the inverse function is

  $C^{-1}(x)=\frac{x-600}{70}$

b.

To determine

To find: The quantities represented by x and $C^{-1}(x)$ in the context of inverse function.

Answer to Problem 7CYU

In the inverse function, x represents cost in dollars for Dwayne for first season and $C^{-1}(x)$ represents the number of games Dwayne attends.

Explanation of Solution

Given information: $C^{-1}(x)=\frac{x-600}{70}$

In the inverse function x represents cost in dollars for Dwayne for first season and $C^{-1}(x)$ represents the number of games Dwayne attends.

c.

To determine

To find: The number of games for the total cost for the season is $950.

Answer to Problem 7CYU

Number of games attended is 5.

Explanation of Solution

Given information: In this part the total cost $C(x)$ is $950 .

Calculation:

Plug in $C(x)$ as $950 then solve it for ‘ x’

  $950=600+70x$

Subtract both sides 600,

  $350=70x$

Divide both sides by 70.

  $x=5$

Conclusion: Number of games attended is 5.