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 do you find the inverse of a function algebraically?

Back

To find the inverse of a function, swap the x and y in the equation and solve for y.

Front

What is the horizontal line test (HLT)?

Back

The horizontal line test is a method to determine if a function has an inverse that is also a function. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse that is a function.

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) = (x - 3)/2.

Front

What does it mean if f^-1(x) is not a function?

Back

It means that the original function f(x) does not pass the horizontal line test, resulting in multiple outputs for at least one input.

Front

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

Back

To verify, check if f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Front

What is the inverse of f(x) = -4x - 12?

Back

f^-1(x) = -1/4x - 3.

Front

What is the graph of a function and its inverse?

Back

The graph of a function and its inverse are symmetric with respect to the line y = x.

Front

If f(x) = x², does it have an inverse?

Back

No, f(x) = x² does not have an inverse that is a function because it fails the horizontal line test.