MATH 121
INVERSE FUNCTIONS

 A.   Determine whether each of the following functions has an inverse function.  If the inverse exists, sketch the function and its inverse on the same set of axes.

1.

2.

3.

4.

5.

6.

7.

B.               In each of the following, find f-1(x). Then graph y = f(x) and f-1(x).

1.   y = 4x - 1

2.   3x + y = 2

3.   x – 2y = 6

C.   Which of the following functions have an inverse?  Write the equations for the inverse function if it exits.

1.   y = x2

4. 

7.  

2.   f(x) = x3 - 1

5.  y = 3

8. 

3.  

6.   y = |x - 1|

 

D. In each of the following, find f-1(x).  Find the domain and range of f(x) and f-1(x).

1. 

2. 

3. 

INVERSE FUNCTIONS (ANSWERS)

A.

1.

2. no

3.

4.

5.no

6.

7.

 

original

inverse

B.

1. 

2. 

3.   f  - 1(x) = 2x + 6

C.  

1.  , no

4.  , yes

7. , no

2.

5.  x = 3, no

8.  , yes

3. , yes

Note: the function is its own inverse

6.   x = |y - 1|, no  
Note: }will give same values for x so an “x” is repeated.

D.

1. 

f (x): D=R, x ≠ -2
   R= R, y ≠ 2

f -1(x): D= R, x ≠ 2
   R= R, y ≠ -2

2. 

f (x): D= R, x ≠ 1
   R= R,  y ≠ -1 

f -1(x):D= R, x ≠ -1
   R= R, ≠ 1

3.

f (x):D= R, x ≠ 0
   R= R, y ≠ -3

f -1(x):D= R, x ≠ -3
    R= R, y ≠ 0