Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if the function takes an input x to an output y, the inverse function takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, switch x and y, and then solve for y.

Front

What does it mean to find the inverse of a function?

Back

It means the x's and y's are switched.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^{-1}(x).

Front

If f(x) = 2x + 3, what is f^{-1}(x)?

Back

f^{-1}(x) = \frac{x - 3}{2}.

Front

What is the relationship between the graphs of a function and its inverse?

Back

The graphs of a function and its inverse are reflections of each other across the line y = x.

Front

How do you graph the inverse of a function?

Back

To graph the inverse, switch the x and y coordinates of each point on the original graph.

Front

Back

Front

What is the domain of an inverse function?

Back

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

Front

What is the range of an inverse function?

Back

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