Question

Graphs of 3 functions are shown below. In two or more sentences, explain whether or not the inverse of each graph is a function.

Answer 1

• Graph 1 ---> the inverse is not a function.
• Graph 2 ---> The inverse is a function.
• Graph 3 ---> the inverse is a function.

How to know if the inverse of a function is also a function?

The inverse of a function is only a function, if the function is one-to-one.

Remember that for a function:

f(x) = y

The inverse is defined as:

f⁻¹(y) = x

So, if there are two values x₁ and x₂ such that:

f(x₁) = f(x₂) = y

Then.

f⁻¹(y) = x₁ or x₂

Which means that it is not a function.

From this, we can see that:

Graph 1 ---> the inverse is not a function.

Graph 2 ---> The inverse is a function.

Graph 3 ---> the inverse is a function.