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 is the inverse of a function denoted?

Back

The inverse of a function f(x) is denoted as f^-1(x).

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other over the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

What does it mean for two functions to be inverses?

Back

Two functions f(x) and g(x) 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

How can you find the inverse of a function algebraically?

Back

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

Tags

CCSS.HSF-BF.B.4A

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

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is obtained by reflecting the graph of the original function over the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(3) = 7, what is f^-1(7)?

Back

f^-1(7) = 3.

Tags

CCSS.HSF-BF.B.4C

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The line y = x serves as the line of reflection for a function and its inverse.

Tags

CCSS.HSF-BF.B.4B