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 graphical representation of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

What is the line of reflection for inverse functions?

Back

The line of reflection for inverse functions is y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

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

Front

How can you verify if two functions are inverses?

Back

To verify if two functions are inverses, check if f(g(x)) = x and g(f(x)) = x.

Tags

CCSS.HSF-BF.B.4B

Front

What is the notation for an inverse function?

Back

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