Inverse Functions

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What is an inverse function?

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An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y back to x.

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How do you find the inverse of a function?

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1. Replace f(x) with y. 2. Switch x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

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What does it mean for a function to be one-to-one?

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A function is one-to-one if it never assigns the same value to two different domain elements. This property is essential for a function to have an inverse.

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What is the relationship between a function and its inverse?

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What is the graphical representation of a function and its inverse?

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How can you verify if two functions are inverses of each other?

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