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