Inverse-Functions (1)

Inverse-Functions (1) - Inverse Functions If two functions...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Inverse Functions If two functions f(x) and g(x) are defined so that (f ο g)(x) = x and (g ο f)(x) = x we say that f(x) and g(x) are inverse functions of each other. Description Of The Inverse Function: Functions f(x) and g(x) are inverses of each other if the operations of f(x) reverse all the operations of g(x) in the reverse order and the operations of g(x) reverse all the operations of f(x) in the reverse order. Example: The function g(x) = 2x + 1 is the inverse of f(x) = (x – 1)/2 since the operation of multiplying by 2 and adding 1 in g(x) reverses the operation of subtracting 1 and dividing by 2. Likewise, the f(x) operations of subtracting 1 and dividing by 2 reverse the g(x) operations of doubling and adding 1. Example: Find a function g(x) that reverses the operations of f(x) = x 3 – 1 that is also the inverse of f(x). Then, verify that f(x) and g(x) are inverses of each other by showing that (f ο g)(x) = x and (g ο f)(x) = x. We need to reverse the operations of cubing and subtracting 1 in reverse order . So we start by adding 1. Then we take the cube root. The function g(x) that corresponds to this is TIP: You should be able to plug in a value of x in one function and get a y-value. Then plug that y-value into the inverse function and you should get back your original value of x. If not, then you don’t have the correct inverse function. Procedure For Finding The Inverse Function To find the correct inverse function of f(x) every time, you can use this procedure: 1. Replace f(x) with y. 2. Switch each x with each y. 3. Solve for y. The resulting function of x will be your inverse
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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Example: Use the previous procedure to find the inverse of the function f(x) = 3x – 5. First, rewrite at y = 3x – 5. Next switch x & y and rewrite as x = 3y – 5 Now solve for y. x + 5
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This note was uploaded on 11/05/2011 for the course ANTHRO 101 taught by Professor Crandall during the Fall '09 term at BYU.

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Inverse-Functions (1) - Inverse Functions If two functions...

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