Inverse Functions – Investigation
Name: ________________________ Date: ___________________ Period: ____________
Algebra 2 Section 6.7: Inverse Functions Notes
Step 1: Find the ordered pairs for[pic]. Complete the chart below.
|[pic] |[pic] |[pic] |[pic] |[pic] |[pic] |
|[pic] | | | | | |
Step 2: Interchange the x- and y- coordinates from step 1.
|[pic] | | | | | |
|[pic] | | | | | |
Step 3: Choose two of the ordered pairs from the table in step 2 and find the equation of the line.
Name this line[pic].
[pic]__________________________
Step 4: For[pic], interchange the variables [pic] and [pic] then solve for [pic] in terms of [pic].
Call this new function[pic].
[pic]__________________________
What do you notice about [pic] and[pic]? Why do you think this is?
Step 5: Use [pic] and[pic] from above to find:
a) [pic] b) [pic]
• If [pic] and [pic] are inverses of each other, then [pic] always equals _____________
and [pic] always equals ______________.
• The function and its inverse always reflect over the line _____________________.
Algebraically, find the inverse of the following functions.
1. [pic] 2. [pic]
3. [pic] 4. [pic]
Finding Non-Linear Inverses Algebraically:
7. [pic] 8. [pic]
9. [pic] 10. [pic]
11. [pic] 12. [pic]
13. Determine if the inverse of each function is also a function.
a) b)
c) d)
[pic] [pic]
14. Prove that f(x) and g(x) are inverses of each other.
[pic]
[pic]
-----------------------
Horizontal Line Test
If a horizontal line drawn through a graph hits more than one point, then the inverse is not a function.
Composition and Inverses
If f and [pic] are inverses of each other, then [pic]
................
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