Question

the monthly cost C (in dollars) a cell phone carrier charges is C= 0.05m+45, where m is the number of minutes used that exceed 500 minutes per month. Find an equation for the inverse function and interpret its meaning. List any restrictions on the domain and range of the inverse function.

Answer 1

C= 0.05m+45, where m is the number of minutes used that exceed 500 minutes per month.

to find the inverse of the given function , solve the equation for m

C= 0.05m+45

C - 45 = 0.05m

divide by 0.05 on both sides

20C - 900 = m

Inverse function is m = 20C -900

C is the monthly cost. Inverse function gives the number of minutes that exceeds 500 minutes per month.

When number of minutes is 500, then cost is 70

We know number of minutes used that exceed 500 minutes per month

So domain (cost) of inverse function is [70, ∞)

Range (minutes) of inverse function is [500, ∞)