Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes x to y, then f^-1(y) takes y back to x.

Tags

CCSS.HSF-BF.B.4A

Front

How can you determine if two functions are 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 does it mean for functions to be reflected over the line y=x?

Back

If two functions are reflected over the line y=x, their graphs are mirror images of each other across this line.

Tags

CCSS.HSF-BF.B.4B

Front

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

Back

The line y=x serves as a reference line; if the graphs of two functions are symmetric with respect to this line, they are inverses.

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), which denotes the inverse of the function f.

Front

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

Back

f^-1(7) = 3, because the inverse function reverses the input and output.

Tags

CCSS.HSF-BF.B.4C

Front

What is the domain of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

Can a function have an inverse?

Back

A function has an inverse if it is one-to-one, meaning it passes the horizontal line test.

Front

What is the horizontal line test?

Back

The horizontal line test states that if any horizontal line intersects the graph of a function more than once, the function does not have an inverse.