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Homework: Inverse Functions

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems designed to develop some concepts related to inverse functions.

Exercise 1

On our last “Sample Test,” we did a scenario where Sally distributed two candy bars to each student and five to the teacher. We found a function c(s)c(s) size 12{c \( s \) } {}that represented how many candy bars she distributed, as a function of the number of students in the room.

  • a. What was that function again?
  • b. How many candy bars would Sally distribute if there were 20 students in the room?
  • c. Find the inverse function.
  • d. Now—this is the key part—explain what that inverse function actually represents. Ask a word-problem question that I can answer by using the inverse function.

Exercise 2

Make up a problem like #1. That is, make up a scenario, and show the function that represents that scenario. Then, give a word problem that is answered by the inverse function, and show the inverse function.

For each function, find the domain, the range, and the inverse function.

Exercise 3

y = 2 + 1 x y = 2 + 1 x size 12{y=2+ { {1} over {x} } } {}

Exercise 4

2x + 3 7 2x + 3 7 size 12{ { {2x+3} over {7} } } {}

Exercise 5

2 ( x + 3 ) 2 ( x + 3 ) size 12{2 \( x+3 \) } {}

Exercise 6

x 2 x 2 size 12{x rSup { size 8{2} } } {}

Exercise 7

x 3 x 3 size 12{x rSup { size 8{3} } } {}

Exercise 8

(x3+10)3

Exercise 9

y = 2x + 1 x y = 2x + 1 x size 12{y= { {2x+1} over {x} } } {}

Exercise 10

y = x 2x 1 y = x 2x 1 size 12{y= { {x} over {2x left [ right ]1} } } {}

Exercise 11

“The functions f(x)f(x) size 12{f \( x \) } {} and g(x)g(x) size 12{g \( x \) } {} are inverse functions.” Express that sentence in math, instead of in words (or using as few words as possible).

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