a From the exercise we can identify two points that the function passes through.
B
b Begin by replacing f(x) with y. Then, exchange x and y in the equation and solve for y.
C
c When exchanging x and y, the things they represent also interchange.
D
d Remember that x now represents the total cost.
A
a C(x)=0.3x+29.99
B
b C^(- 1)(x)=10/3x-2999/30
C
cWhat Does x Represent? Total cost. What Does C^(- 1)(x) Represent? Number of minutes.
D
d 63
Practice makes perfect
a If the number of extra minutes is x, the following equation represents the total cost of the bill.
C(x)= mx+ b
In the equation, b represents the fixed fee of the plan and m is the charge for each extra minute above 700 minutes. From the exercise, we know that using 26 extra minutes costs $37.79. Additionally, when using 38 extra minutes the total cost is $41.39. With this information, we can create two points that C(x) passes through.
C(26)=37.79 ⇒ ( 26, 37.79)
C(38)=41.39 ⇒ ( 38, 41.39)
Since we know two points of the line, we can calculate the slope using the Slope Formula.
The slope of the line is 0.3. So far, we have the following equation.
C(x)= 0.3x+ b
To find the value of b, which is the y-intercept, we will substitute one of the known points into the equation and solve for b.
We can now replace y for C^(- 1)(x) to show the inverse of C(x).
C^(- 1)(x)=10/3x-2999/30
c When inverting a function, the items represented by one variable in the given function will be represented by the other variable in the inverse function.
C(x)
C^(-1)(x)
x represents
Number of additional minutes used
Total monthly cost of cell phone package
C represents
Total monthly cost of cell phone package
Number of additional minutes used
d If we substitute x= 48.89 in the inverse function, we can find the number of additional minutes by simplifying the right-hand-side.
