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.

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.

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.

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.

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.

Front

What is the domain of an inverse function?

Back

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

Front

What is the range of an inverse function?

Back

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

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.