Question Video: Finding the Inverse Function of a Given Linear Function Mathematics

Video Transcript

Find the inverse of the function 𝑓 of 𝑥 equals four 𝑥.

The inverse of a function is the opposite. In this case, 𝑥 is being multiplied by four. The opposite of multiplying by four is dividing by four. Therefore, at first glance, it would appear that the inverse function 𝑓 minus one of 𝑥 is 𝑥 divided by four or 𝑥 over four.

Let’s check this answer by using a method we would use for more complicated functions. In order to work out the inverse of any function, we firstly exchange the variables and secondly rearrange the equation to express 𝑦 in terms of 𝑥. The function 𝑓 of 𝑥 equals four 𝑥 can be rewritten as 𝑦 equals four 𝑥. Exchanging the variables allows us to rewrite this as 𝑥 equals four 𝑦. Dividing both sides of this equation by four gives us 𝑦 is equal to 𝑥 divided by four. Therefore, as we have rearranged it to express 𝑦 in terms of 𝑥, we can say that the inverse function 𝑓 minus one of 𝑥 is equal to 𝑥 divided by four.

This confirms our initial thoughts that the inverse of the function four 𝑥 is 𝑥 divided by four.