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,

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