### Video Transcript

What is the inverse of the function π¦ equals seven π₯ minus five?

First, letβs consider what an inverse is. Formally, we could say if π¦ equals π of π₯, then π₯ equals the inverse function evaluated at π¦. Whatβs happening here is that weβre switching the input and the output. For the function π of π₯, the input values are π₯ and the output values are π¦. For the inverse, the input values will be π¦ and the output values will be π₯.

Thereβs an algebraic method we sometimes use for finding this function. This process involves two steps. First, we exchange the variables. That means we switch the π₯ and π¦. And in step two, we rearrange to express π¦ in terms of π₯. We know that π¦ equals seven π₯ minus five. But for our inverse function, π₯ is going to equal seven π¦ minus five. This completes step one.

However, we still prefer to write the equation so that it is in the form π¦ equals some π₯-value. And that means we want to rearrange this equation so the π¦ is by itself. To do that, we add five to both sides of the equation, and we now have π₯ plus five equals seven π¦. So we divide both sides of the equation by seven. On the left, we have π₯ plus five over seven. And on the right, we have π¦ by itself, which completes our second step and makes our inverse function π¦ equals π₯ plus five over seven.