Inverse Function

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What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x.

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CCSS.HSF-BF.B.4A

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

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Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

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CCSS.HSF-BF.B.4B

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What is a one-to-one function?

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A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs map to the same output.

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CCSS.HSF-LE.A.1B

Front

What is the horizontal line test?

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The horizontal line test is a method to determine if a function is one-to-one. If any horizontal line intersects the graph more than once, the function is not one-to-one.

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What does it mean for a function to be not a function?

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A relation is not a function if at least one input is associated with more than one output.

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CCSS.8.F.A.1

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What is the relationship between the graphs of a function and its inverse?

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

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CCSS.HSF-BF.B.4C

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What is the domain of an inverse function?

Back

The domain of the inverse function is the range of the original function.

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CCSS.HSF-BF.B.4C

Front

What is the range of an inverse function?

Back

The range of the inverse function is the domain of the original function.

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CCSS.HSF-BF.B.4C

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Can a function have more than one inverse?

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No, a function can have at most one inverse if it is one-to-one.

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CCSS.HSF-BF.B.4D

Front

What is the notation for an inverse function?

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The notation for an inverse function is f⁻¹(x), where f is the original function.