Inverse Functions

Front

What is 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 function takes y back to x.

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CCSS.HSF-BF.B.4A

Front

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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CCSS.HSF-BF.B.4A

Front

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

Back

It means the x's and y's are switched.

Tags

CCSS.HSF-BF.B.4A

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^{-1}(x).

Front

If f(x) = 2x + 3, what is f^{-1}(x)?

Back

f^{-1}(x) = \frac{x - 3}{2}.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

The graphs 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

Front

How do you graph the inverse of a function?

Back

To graph the inverse, switch the x and y coordinates of each point on the original graph.

Tags

CCSS.HSF-BF.B.4C

Front

Back

Tags

CCSS.HSF-BF.B.4A

Front

What is the domain of an inverse function?

Back

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

Tags

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.

Tags

CCSS.HSF-BF.B.4C