Math 171 Group Worksheet over Inverses (1.5)
January 15, 2016
Credit given for work shown.
No calculators needed.
Name
1. Let C = f ( q ) = 400 + 0 .
2 q give the cost in dollars to manufacture q kg of a chemical. Which of the following statement(s) correctly explain the meaning of f
− 1
( C )? Circle all that apply.
A. The cost of manufacturing one kg. of the chemical.
B. The number of kgs. of the chemical someone can purchase with C dollars.
C. The number of kgs. of chemical that can be manufactured for each 1 dollar spent.
D. The number of kgs. of the chemical that can be manufactured with C dollars.
E. The cost of manufacturing C kgs. the chemical.
F. None of the above
2. Consider the function g ( x ) represented by the table below on the left. Complete the table of values for the INVERSE, g
− 1
( y ), in the table below on the right: x -3 -2 -1 0 1 2 3 y -3 -2 -1 0 1 2 3 g ( x ) -2 0 1 2 -3 3 -1 g
− 1
( y )
3. Let f ( t ) = 3 t + 2. Solve each of the following equations exactly for t .
(a) f ( t ) = 4 (c) f
− 1
( t ) = 4
(b) ( f ( t ))
− 1
= 4 (d) f t
− 1 = 4
4. Let f be a linear function with slope m with m = 0. What is the slope of the inverse function f
− 1
?

5. Let f ( x ) = 1 +
√ x . Determine the inverse function of f .
f
− 1
( y ) =
The domain of f :
The domain of f
− 1
: and range of
6. If f ( x ) = x
3
+ 5 x − 2, then f
− 1
(4) =
[Note: You cannot solve this algebraically.]
.
f : and range of f
− 1
:
7. Show that f ( x ) = x + 1 x − 1 is its own inverse by computing f ( f ( x )).
8. In the theory of relativity, the mass of a particle with speed v is m = m ( v ) = m
0 p
1 − v 2 /c 2 where m
0 is the rest mass of the particle and inverse function v ( m ) and explain its meaning.
c is the speed of light in a vacuum. Find the