Inverse Functions (Tables & Graphs)

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.

Front

How can you determine if two functions are inverses of each other?

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.

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.

Front

What does it mean if two functions are not inverse functions?

Back

If f(g(x)) ≠ x or g(f(x)) ≠ x for any x in the domain, then the functions are not inverses.

Front

How do you find the inverse of a function algebraically?

Back

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

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.

Front

What is the significance of the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one, which is necessary for it to have an inverse.

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.

Front

How do you graph the inverse of a function?

Back

To graph the inverse, reflect the graph of the original function across the line y = x.