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# Inverse Function

### Module 22

What is an one-to-one function? A one-to-one function is when each x-value corresponds to only 1 y-value, and each y-value corresponds to only 1 x-value.
How can you check on a graph if an equation is an one-to-one function? You can do horizontal line test. If every horizontal line intersects only once, then the function is a one-to-one function.
What type of lines are one-to-one functions? All lines are one-to-one functions except for horizontal or vertical lines.
What is the inverse to an one-to-one function? The inverse of an one-to-one function f(x) is f^-1 that consists of all ordered pairs (y,x), while f consists of (x,y).
What are the steps to finding the inverse of an one-to-one function f(x)? Step 1: Replace f(x) with y Step 2; Change x to y and y to x Step 3; Solve the equation for y Step 4; Replace y with the notation f^-1(x)
Is there a way to check if f(x) is an one-to-one function? Yes, if f(x) is an one-to-one function, then the inverse of f(x) is the function f^-1. Or where (f^-1 o f)(x)=x and (f o f^-1)(x)=x
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