Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation 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?

Back

1. Replace f(x) with y. 2. Switch x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Tags

CCSS.HSF-BF.B.4A

Front

If f(x) = x + 5, what is f⁻¹(x)?

Back

f⁻¹(x) = x - 5.

Tags

CCSS.HSF-BF.B.4A

Front

If f(x) = 3x - 5, what is f⁻¹(x)?

Back

f⁻¹(x) = (x + 5)/3.

Tags

CCSS.HSF-BF.B.4A

Front

If f(x) = 2x + 4, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 4)/2.

Tags

CCSS.HSF-BF.B.4A

Front

If f(x) = 4 - 2x, what is f⁻¹(x)?

Back

f⁻¹(x) = 2 - ½x.

Tags

CCSS.HSF-BF.B.4A

Front

What is the first step in finding the inverse of a relation?

Back

Replace f(x) with y.

Tags

CCSS.HSF-BF.B.4A

Front

What do you do after switching x's and y's when finding an inverse?

Back

Solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What is the notation for an inverse function?

Back

f⁻¹(x) denotes the inverse of the function f(x).

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.

Tags

CCSS.HSF-BF.B.4C