Test: Inverse Functions

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What is an inverse function?

Back

An inverse function reverses the operation of the original function. If the function is 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 linear function?

Back

To find the inverse of a linear function, swap x and y, then solve for y. For example, for y = 2x + 7, swap to get x = 2y + 7, then solve for y to find the inverse.

Tags

CCSS.HSF-BF.B.4A

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Back

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CCSS.HSF-BF.B.4A

Front

What is the inverse of the points (1,3), (2,4), (6,8)?

Back

The inverse points are (3,1), (4,2), (8,6).

Tags

CCSS.HSF-BF.B.4C

Front

How do you find the inverse of a quadratic function?

Back

To find the inverse of a quadratic function, isolate y, swap x and y, and solve for y. Ensure the function is one-to-one or restrict its domain.

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CCSS.HSF-BF.B.4D

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Back

Tags

CCSS.HSF-BF.B.4A

Front

What is the relationship between a function and its inverse?

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A function and its inverse are reflections across the line y=x.

Tags

CCSS.HSF-BF.B.4C

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True or False: The inverse of an exponential function is its reflection across the x-axis.

Back

False. The inverse of an exponential function is its reflection across the line y=x.

Tags

CCSS.HSF-BF.B.4A

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What does it mean for two functions to be inverses?

Back

Two functions are inverses if their compositions yield the identity function: f(f^(-1)(x)) = x and f^(-1)(f(x)) = x.

Tags

CCSS.HSF-BF.B.4B