# Question Video: Determining Whether a Function Has an Inverse Mathematics

Does the function 𝑓, where 𝑓 = {(5, 3), (9, 7), (11, 10)}, have an inverse?

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### Video Transcript

Does the function 𝑓, where 𝑓 is the set of ordered pairs five, three; nine, seven; and 11, 10, have an inverse?

We know that any function has an inverse if it is one to one. This means that each 𝑥-value has a unique 𝑦-value. In this question, we have three ordered pairs: five, three; nine, seven; and 11, 10. The first value in each of these ordered pairs is our 𝑥-value, and the second value is the 𝑦-value. We can sketch this using an arrow diagram. We have three unique input or 𝑥-values in our function. They are five, nine, and 11. These are paired with three unique output or 𝑦-values of three, seven, and 10. This means that the function is one to one and therefore does have an inverse.

Whilst it is not required in this question, the inverse function of 𝑓 will contain the ordered pairs three, five; seven, nine; and 10, 11.

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