Calculus Finding the Inverse of Functions

Math 115 – Graded Assignment 3 Sections 01 & 02 Due 9/14/2023 Name: ___________________________________ Score: ___ /10 1. Let f ( x= ) 3 x − 2. a. Does f have an inverse? Explain. b. Find the inverse of the function f. c. Graph f and f −1 in the same coordinate system. Verify that the graphs of f and f −1 are symmetric with respect to the line y = x. 2. On a certain route, an airline carries 9000 passengers per month, each paying $150. A market survey indicates that for each $1 decrease in the ticket price, the airline will gain 50 passengers. a. Express the number of passengers per month, N, as a function of the ticket price, x. Answer: N ( x) = ___________________________ b. Express the monthly revenue for the route, R, as a function of the ticket price, x. Answer: R ( x) = ___________________________ 3. A rain gutter is made from sheets of aluminum that are 20 inches wide. As shown in the figure, the edges are turned up to form right angles. Express the cross-sectional area of the gutter, A, as a function of its depth, x. Answer: A( x) = ___________________________ 4. You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller playgrounds by placing the fencing parallel to one of the sides. Express the area of the playground, A, as a function of one of its dimensions, x. Answer: A( x) = ___________________________