Inverse Functions

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

If f(2) = -1, what is g(-1)?

Back

g(-1) = 2, because f and g are inverse functions.

Tags

CCSS.HSF-BF.B.4C

Front

What is the relationship between a function and its inverse?

Back

For a function f and its inverse f⁻¹, the following holds: f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

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 inverse of f(x) = 3x + 5?

Back

f⁻¹(x) = (x - 5)/3.

Tags

CCSS.HSF-BF.B.4A

Front

If f⁻¹(-25) = 7, what is f(7)?

Back

f(7) = -25, because f and f⁻¹ are inverse functions.

Tags

CCSS.HSF-BF.B.4C

Front

What does it mean if two functions are inverses of each other?

Back

It means that applying one function followed by the other returns the original input.

Tags

CCSS.HSF-BF.B.4B

Front

What is the inverse of f(x) = -4x - 12?

Back

f⁻¹(x) = -1/4x - 3.

Tags

CCSS.HSF-BF.B.4A

Front

If g(1) = -2, what is f(-2)?

Back

f(-2) = 1, because f and g are inverse functions.

Tags

CCSS.HSF-BF.B.4C

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.

Tags

CCSS.HSF-BF.B.4C