Inverse - If f(x) maps x to y, then the inverse of f(x) maps y to x.
- Denoted as f-1(x).
To Find an Inverse
1) Switch the x and the y-values.
2) Resolve for y.
3) Don't forget that if you take an even root, you need the +.
If you take an odd root, you don't need the +.
Example
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Horizontal Line Test
- Tells you if a function has an inverse. In mathematical words, it
tells you if a function is injective.
- Works the same as the Vertical Line Test, but you use horizontal
lines instead.
Example
Are the following functions injective?
A) y = -x + 9
B) y =
2x + 7
C) y = 2x2 + 9
D) y = - | 2x - 7 |
To Verify Functions Are Inverses 1) Take f(g(x)). You should get x.
2) Take g(f(x)). You should get x.
Example
Verify the functions are inverses.
Example
Verify the functions are inverses.
Example
Verify the functions are inverses.
HOMEWORK
Worksheet 1C