inverse functions. one to one functions functions that have inverses functions have inverses if f(x...
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![Page 1: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/1.jpg)
Inverse Functions
![Page 2: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/2.jpg)
One to one functions
Functions that have inverses Functions have inverses if f(x1) ≠ f(x2) when
x1 ≠ x2
Graphically you can use the horizontal line test to determine if a function is one to one
- no horizontal line will intersect the graph more than once if the function is one to one
![Page 3: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/3.jpg)
Example: Determine if the following are one to one
f(x) = x3
f(x) = x2
![Page 4: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/4.jpg)
Inverse Function f-1
f-1(y) = x f(x) = y
Domain of f-1 is the range of f
Range of f-1 is the domain of f
![Page 5: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/5.jpg)
Example
If f(1) = 5, f(3) = 7, and f(8) = -10, find f-1(7), f-1(5), and f-1(-10)
![Page 6: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/6.jpg)
Example
Find the inverse of f(x) = x3 + 2
![Page 7: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/7.jpg)
Drawing the Inverse
The graph of f-1 is obtained by reflecting the graph of f about the line y = x
On calculator plot f, then use “DRAW” menu, #8 (DrawInv)
![Page 8: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/8.jpg)
Example:
Draw inverse of f(x) = √(-1 – x)
![Page 9: Inverse Functions. One to one functions Functions that have inverses Functions have inverses if f(x 1 ) ≠ f(x 2 ) when x 1 ≠ x 2 Graphically you can use](https://reader036.vdocuments.site/reader036/viewer/2022082506/5697c0081a28abf838cc6e0c/html5/thumbnails/9.jpg)
Example
Show that the function f(x) = √(x3 + x2 + x + 1) is one to one for both f and f-1