Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(x) = y, then f⁻¹(y) = x.

Tags

CCSS.HSF-BF.B.4A

Front

How do you find the inverse of a function algebraically?

Back

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

Find the inverse of f(x) = 3x + 8.

Back

f⁻¹(x) = (x - 8) / 3.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

It means to switch the x's and y's in the function.

Tags

CCSS.HSF-BF.B.4A

Front

Find the inverse of f(x) = 4 - 2x.

Back

f⁻¹(x) = 2 - ½x.

Tags

CCSS.HSF-BF.B.4A

Front

Find the inverse of f(x) = 2x + 4.

Back

f⁻¹(x) = (x - 4) / 2.

Tags

CCSS.HSF-BF.B.4A

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = x², what is the inverse function?

Back

f⁻¹(x) = √x (for x ≥ 0).

Tags

CCSS.HSF-BF.B.4A

Front

What is the domain of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

What is the range of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C