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 algebraically?

Back

To find the inverse of a function, swap the x and y in the equation and solve for y.

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

Front

If f(1) = 3, what is f⁻¹(3)?

Back

f⁻¹(3) = 1.

Tags

CCSS.HSF-BF.B.4C

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x).

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

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

Back

f⁻¹(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What points does f⁻¹(x) go through if f(x) goes through (2, 5)?

Back

f⁻¹(x) goes through (5, 2).

Tags

CCSS.HSF-BF.B.4C

Front

What is the domain of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

What is the range of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C