# Inverse Functions

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A function is a relationship where each x value has only one y value associated with it. Each y value may or may not have only one x value associated with it.

For example: y = x^{2} If 2 is substituted in for x y = 4; if -2 is substitute for x y = 4

Therefore y = 4 has two x values associated with it x = 2 and x = -2. expression in ordered pair notation (2,4),(-2,4)

Every y value in the parabola y = x^{2} as seen in the below graph will have two x values.

Another example is if x = 3 y = 9 and if x = -3 y still = 9 (3,9),(-3,9)

IMPORTANT - There are functions where every y value has only one x value assigned to it and each x value has only one y value. These are called one to one functions.

For example y = x^{3} is a one to one function. If 2 is substituted in for x y = 8; if -2 is substitute for x y = -8 (2,8),(-2,-8)

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