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.

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

If f(1) = 4, what is f⁻¹(4)?

Back

f⁻¹(4) = 1.

Front

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

Back

The coordinates of a function (x, y) become (y, x) in its inverse.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, ensuring that it has an inverse.

Front

How can you tell if a function is one-to-one using its graph?

Back

A function is one-to-one if any horizontal line intersects the graph at most once.

Front

What is the horizontal line test?

Back

The horizontal line test is a method to determine if a function is one-to-one by checking if any horizontal line intersects the graph more than once.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

What is the domain of an inverse function?

Back

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