Name_________________________________ Date________________
Period_________
QUADRATIC INVERSE FUNCTION WORKSHEET
Steps:
1. Replace f(x) with y.
2. Interchange the x and y in the equation.
3. Solve for y in terms of x.
4. Replace y by f -1(x).
5. It is helpful to use the domain and range of the original function to identify the domain and range of the inverse. The
inverse may or may not be a function. Restrict the domain of the original function to get an inverse function.
Find the inverse of each function. Graph and label the function and its inverse. State the domain and range
of each function and its inverse. Determine whether the inverse is a function.
1)
f ( x)   x  1
2)
f ( x)  x 2  3
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
3)
2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
f ( x)  x 2  4, x  0
4)
10
8
6
6
4
4
2
2
4
6
8 10
8 10
6
8 10
2
8
2
6
y  x  5 , x  5
10
-10 -8 -6 -4 -2
4
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
5) y  ( x  2)2  1
6)
f ( x)   x  2 , x  2
2
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
2
4
6
8 10
-10 -8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8 10
7) Verify by composition that the function in Question #3 and your answer are inverses.
8) Verify by composition that the function in Question #6 above and your answer are inverses.