Linear and Quadratic Inverses

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What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if the function takes an input x to an output y, the inverse takes y back to x.

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How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, switch x and y, and then solve for y.

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What does it mean to find the inverse of a function graphically?

Back

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Back

The function does not have an inverse because it is not one-to-one.

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Front

What is the significance of the horizontal line test in relation to inverses?

Back

The horizontal line test determines if a function is one-to-one; if any horizontal line intersects the graph more than once, the function does not have an inverse.

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What does it mean to switch x's and y's when finding an inverse?

Back

Switching x's and y's means that for every point (a, b) on the original function, the point (b, a) will be on the inverse function.