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 and produces x.

Front

How can you visually determine if a function is one-to-one?

Back

You can use the horizontal line test. If any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

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

Find the inverse of the function f(x) = 2x + 3.

Back

f^-1(x) = (x - 3)/2.

Front

Find the inverse of the function f(x) = 5x - 7.

Back

f^-1(x) = (x + 7)/5.

Front

What is the inverse of the function f(x) = 3x - 5?

Back

f^-1(x) = (x + 5)/3.

Front

Find the inverse of the function f(x) = (x - 5)/3.

Back

f^-1(x) = 3x + 5.

Front

Are the functions f(x) = x + 2 and g(x) = x - 2 inverse functions?

Back

No, they are not inverse functions.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse 'undo' each other. If f(f^-1(x)) = x and f^-1(f(x)) = x, then they are inverses.

Front

What is the notation for an inverse function?

Back

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