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, switch the x and y in the equation and solve for y.

Front

What is the notation for the inverse of a function g(x)?

Back

The notation for the inverse of g(x) is g^-1(x).

Front

If f(1) = 4, what is f^-1(4)?

Back

f^-1(4) = 1.

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the first step in finding the inverse of a function?

Back

The first step is to switch x and y in the equation.

Front

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

Back

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

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse if it is a one-to-one function.

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

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

Back

No, f(x) = x² is not one-to-one, so it does not have an inverse.