# Video: AQA GCSE Mathematics Higher Tier Pack 1 β’ Paper 2 β’ Question 19

AQA GCSE Mathematics Higher Tier Pack 1 β’ Paper 2 β’ Question 19

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### Video Transcript

Consider the function π of π₯ is equal to π₯ over seven. Circle the expression which is equal to the inverse of π of π₯. Is it negative π₯ over seven, seven over π₯, π₯ over seven, or seven π₯?

Letβs begin by recapping the terminology. For a function π of π₯, this means the inverse of the function. Sometimes, as you might have noticed in this case, itβs quite simple to spot the inverse since inverse means opposite. But letβs look at the method we can use.

To find the inverse, we rewrite our function as π¦ is some function of π₯. This time, thatβs π¦ equals π₯ over seven. We then switch the π₯ and the π¦ to get π₯ is equal to π¦ over seven.

To find the inverse, we make π¦ the subject. To make π¦ the subject here, we need to multiply both sides of the equation by seven. And that gives us seven π₯ is equal to π¦.

When we have successfully made π¦ the subject, we can replace the π¦ with the notation for the inverse, which was as shown. So the inverse for this function is seven π₯.

And remember we said that the inverse means opposite. And the original function was telling us that for any value of π₯, we divide it by seven. We know the opposite to that is to multiply it by seven.

So we could have spotted straightaway that the inverse was seven π₯. However, this method is a really nice method for slightly more complicated examples of functions.

The expression which is equal to the inverse of π is seven π₯.