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 inverse of f(x) = -4x - 12?

Back

f^-1(x) = -1/4x - 3.

Tags

CCSS.HSF-BF.B.4A

Front

What operation allows us to verify if two functions are inverses?

Back

Composing the functions. If f(f^-1(x)) = x and f^-1(f(x)) = x, then they are inverses.

Tags

CCSS.HSF-BF.B.4B

Front

If f(x) = x + 5, what is f^-1(x)?

Back

f^-1(x) = x - 5.

Tags

CCSS.HSF-BF.B.4A

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

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

Can a function have more than one inverse?

Back

No, a function can have at most one inverse unless it is not a one-to-one function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, ensuring that it has an inverse.