# Video: AQA GCSE Mathematics Higher Tier Pack 1 • Paper 2 • Question 19

AQA GCSE Mathematics Higher Tier Pack 1 • Paper 2 • Question 19

01:38

### Video Transcript

Consider the function 𝑔 of 𝑥 is equal to 𝑥 over seven. Circle the expression which is equal to the inverse of 𝑔 of 𝑥. Is it negative 𝑥 over seven, seven over 𝑥, 𝑥 over seven, or seven 𝑥?

Let’s begin by recapping the terminology. For a function 𝑔 of 𝑥, this means the inverse of the function. Sometimes, as you might have noticed in this case, it’s quite simple to spot the inverse since inverse means opposite. But let’s look at the method we can use.

To find the inverse, we rewrite our function as 𝑦 is some function of 𝑥. This time, that’s 𝑦 equals 𝑥 over seven. We then switch the 𝑥 and the 𝑦 to get 𝑥 is equal to 𝑦 over seven.

To find the inverse, we make 𝑦 the subject. To make 𝑦 the subject here, we need to multiply both sides of the equation by seven. And that gives us seven 𝑥 is equal to 𝑦.

When we have successfully made 𝑦 the subject, we can replace the 𝑦 with the notation for the inverse, which was as shown. So the inverse for this function is seven 𝑥.

And remember we said that the inverse means opposite. And the original function was telling us that for any value of 𝑥, 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 𝑥. However, this method is a really nice method for slightly more complicated examples of functions.

The expression which is equal to the inverse of 𝑔 is seven 𝑥.