2.10  Inverse Functions

College Algebra: One Step at a Time,  Pages 324 - 332:   #5, 6, 7, 11, 14

Dr. Robert J. Rapalje

Seminole Community College

Sanford, FL  32773

5.   Show that  and  are inverse functions of one another. 

Solution:  Note:  In this solution, I tried to put in a few extra steps to make it easier to follow.  Unfortunately, it makes the problem longer, and perhaps the length of this solution may make it somewhat intimidating.  Just realize that all of these steps are NOT necessary.  Use the ones you need.  Don't despair!!  The other problems in this section are easier.

First find                       .

            =

This is a complex fraction, which can be simplified by a couple of different methods.  I think it works nicely if you multiply numerator and denominator by the LCD which is .  It may help to think of this as .

For the second part, you must find

Recall that                

Now              

=

This is also a complex fraction, which can be simplified by a couple of different methods.  Again, I think it works nicely if you multiply numerator and denominator by the LCD which is . 

6.  Show that  and  are inverse functions of one another. 

First find      .

This is a complex fraction, which can be simplified by a couple of different methods.  I think it works nicely if you multiply numerator and denominator by the LCD which is .  It may help to think of this as .

For the second part, you must find  

Recall that                                     

Now              

This is also a complex fraction, which can be simplified by a couple of different methods.  Again, I think it works nicely if you multiply numerator and denominator by the LCD which is . 

p. 327.  # 7.  Show that  and  are inverse functions of one another. 

First find      .

For the second part, you must find

Recall that                                   

Now              

Page 328. # 11.  Find  for    

Solution:  Let

Step 1:       Interchange the x and y:   

Step 2:     Solve for y!

                      Multiply both sides by 2: 

                      Subtract 3                          

                      Divide both sides by 5:     

                      Therefore,                 

Page 329. # 14.  Find  for    

Solution:  Let

Step 1:      Interchange the x and y:      

Step 2:     Solve for y!

                     Multiply both sides by 5y: 

                     Get y terms on left side:     

                     Factor out the y:                          

                     Divide both sides by 5x-3:     

                     Therefore,