Inverse Function Practice

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Define an inverse function.

Back

An inverse function reverses the operation of the original function. If the function is denoted as f(x), its inverse is denoted as f^{-1}(x), such that f(f^{-1}(x)) = x.

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How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, follow these steps: 1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^{-1}(x).

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What is the general form of a linear function?

Back

A linear function can be expressed as f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is the relationship between a function and its inverse?

Back

The function and its inverse are reflections of each other across the line y = x.

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

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To verify, check if f(f^{-1}(x)) = x and f^{-1}(f(x)) = x for all x in the domain.

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What is the significance of the horizontal line test?

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The horizontal line test determines if a function is one-to-one, which is necessary for it to have an inverse.