Inverse Function Practice

Front

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.

Tags

CCSS.HSF-BF.B.4A

Front

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).

Tags

CCSS.HSF-BF.B.4A

Front

Back

Tags

CCSS.HSF-BF.B.4A

Front

Back

Tags

CCSS.HSF-BF.B.4A

Front

Back

Tags

CCSS.HSF-BF.B.4A

Front

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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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CCSS.HSF-BF.B.4C

Front

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

Back

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

Tags

CCSS.HSF-BF.B.4B

Front

Back

Tags

CCSS.HSF-BF.B.4A

Front

What is the significance of the horizontal line test?

Back

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