Worksheet – Inverse Functions
1. A manufacturer makes t-shirts and has found that if they charge $20.00 for their t-shirts
they will sell 900 t-shirts every week. If they drop the price to $17.00, they will sell 1100
A. If the quantity of t-shirts sold is a function of the price in which they can sell the t-
shirts, find the linear equation that models this problem. Use p to represent price and
q f ( p) to represent quantity sold.
B. Find and interpret f (15).
C. Give a practical interpretation of the slope.
D. Find both the horizontal and vertical intercepts.
E. Give practical interpretations of both of these intercepts.
F. Find the logical domain and range of this function.
G. Sketch the graph of this function.
H. Find the inverse of the equation you found in part A.
I. What does the inverse function tell you, in terms of price and quantity sold?
J. Interpret the slope of the inverse function.
K. Find the vertical and horizontal intercepts of the inverse functions.
L. Give the practical interpretations of the intercepts of the inverse function.
M. Find and interpret f (950 ).
2. The life expectancy, L , of a child, at birth can be modeled by the formula
L f (t )
where t is the year of birth and t 0 corresponding to 1950.
A. Find a formula for the inverse function.
B. What does the inverse function tell you, in terms of life expectancy and year of birth?
C. Estimate f (70 ) and give a practical interpretation.