The document discusses inverse functions and how to find them. It provides examples of inverse pairs of functions and explains that for functions f and g to be inverses, f(g(x)) = x and g(f(x)) = x. It also notes that the horizontal line test determines whether the inverse of a function is itself a function. The document shows how to take a function, find its inverse by swapping x and y and solving for y, and provides examples of doing this for various functions.

1. 7.5 inverse functions.notebook January 22, 2013
An Inverse Relation switches input and output values.
Input x ­2 ­1 0 1 2
Output y ­4 ­2 0 2 4
Input x
Output y
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2. 7.5 inverse functions.notebook January 22, 2013
Functions are Inverse Functions if:
f(g(x)) = x and g(f(x)) = x
Verify that f(x) = x + 3 and g(x) = x ­ 3 are inverse functions.
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3. 7.5 inverse functions.notebook January 22, 2013
Find the inverse of the function f(x) = 2x + 4. To find an inverse function:
1. Replace f(x) with y
2. Switch x and y
3. Solve for y
4. Replace y with f ­1(x)
Find the inverse of the function f(x) = 4x
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4. 7.5 inverse functions.notebook January 22, 2013
Horizontal Line Test
If no horizontal line intersects the graph of a function f more than once,
then the inverse of f is also a function.
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5. 7.5 inverse functions.notebook January 22, 2013
Determine whether the inverse of f(x) = x3 + 1 is a function. Then find the inverse.
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6. 7.5 inverse functions.notebook January 22, 2013
Determine whether the inverse of f(x) = x2, where x ≥ 0, is a function. Graph the inverse.
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