Function Inverses

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y back to 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 f(x), 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

What is the inverse of f(x) = 3x + 2?

Back

f⁻¹(x) = (x - 2) / 3.

Tags

CCSS.HSF-BF.B.4A

Front

What is the inverse of f(x) = 2x - 16?

Back

f⁻¹(x) = (x + 16) / 2.

Tags

CCSS.HSF-BF.B.4A

Front

What is the relationship between a function and its inverse?

Back

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

What is the domain of the 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 the inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

How can you verify if two functions are inverses?

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

What is the inverse of f(x) = x² (for x ≥ 0)?

Back

f⁻¹(x) = √x.

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CCSS.HSF-BF.B.4D

Front

What is the inverse of f(x) = 1/x?

Back

f⁻¹(x) = 1/x.

Tags

CCSS.HSF-BF.B.4A