PRECALCULUS Inverse Relations and Functions. If two relations or functions are inverses, one relation contains the point (x, y) and the other relation.

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Presentation transcript:

PRECALCULUS Inverse Relations and Functions

If two relations or functions are inverses, one relation contains the point (x, y) and the other relation contains the point (y, x). *Their graphs will be symmetric with respect to the line y = x.

Sketch the inverse of the graph:

One-to-One / Horizontal Line Test A function is one-to-one if no two x values have the same y value. We can determine if a function is one-to-one by evaluating the graph of the original function using the Horizontal Line Test. If a horizontal line passes through the graph in more than one point, the function is not one-to-one, and the inverse of the function is not a function.

Determine whether the inverse of each function is a function

Find the inverse of f(x) algebraically.

Find the inverse of h(x) algebraically.

Definition of an Inverse Function

Verify that f(x) and g(x) are inverse functions algebraically.

Extra Practice Write the equation of a function that will have an inverse that is NOT a function.

Extra Practice Write the equation of a function that will have an inverse that IS a function.

Extra Practice