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Inverse Functions

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

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

Exercise 1

We are playing the function game. Every time you give Christian a number, he doubles it and subtracts six.

  • a. If you give Christian a ten, what will he give you back?
  • b. If you give Christian an xx size 12{x} {}, what will he give you back?
  • c. What number would you give Christian, that would make him give you a 0?
  • d. What number would you give Christian, that would make him give you a ten?
  • e. What number would you give Christian, that would make him give you an xx size 12{x} {}?

    Hint for the stuck:

    Try to follow the process you used to answer part (d).

Exercise 2

A television set dropped from the top of a 300' building falls according to the equation: h(t)=30016t2h(t)=30016t2 size 12{h \( t \) ="300" - "16"t rSup { size 8{2} } } {}

h(t)=30016t2h(t)=30016t2 size 12{h \( t \) ="300" - "16"t rSup { size 8{2} } } {}

where tt size 12{t} {} is the amount of time that has passed since it was dropped (measured in seconds), and hh size 12{h} {} is the height of the television set above ground (measured in feet).

  • a. Where is the television set after 0 seconds have elapsed?
  • b. Where is the television set after 2 seconds have elapsed?
  • c. A man is watching out of the window of the first floor, 20' above ground. At what time does the television set go flying by?
  • d. At what time does the television reach the ground?
  • e. Find a general formula t(h)t(h) size 12{t \( h \) } {} that can be used to quickly and easily answer all questions like (c) and (d).

Find the inverse of each function. For each one, check your answer by plugging in two different numbers to see if they work.

Exercise 3

y = x + 5 y = x + 5 size 12{y=x+5} {}

  • Inverse function:
  • Test:
  • Test:

Exercise 4

y = x + 6 y = x + 6 size 12{y=x+6} {}

  • Inverse function:
  • Test:
  • Test:

Exercise 5

y = 3x y = 3x size 12{y=3x} {}

  • Inverse function:
  • Test:
  • Test:

Exercise 6

y = x 4 y = x 4 size 12{y= { {x} over {4} } } {}

  • Inverse function:
  • Test:
  • Test:

Exercise 7

y = 3x + 12 y = 3x + 12 size 12{y=3x+"12"} {}

  • Inverse function:
  • Test:
  • Test:

Exercise 8

y = 100 x y = 100 x size 12{y= { {"100"} over {x} } } {}

  • Inverse function:
  • Test:
  • Test:

Exercise 9

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

  • Inverse function:
  • Test:
  • Test:

Exercise 10

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

  • Inverse function:
  • Test:
  • Test:

Exercise 11

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

  • Inverse function:
  • Test:
  • Test:

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