Question Video: Finding the Inverse of Linear Functions | Nagwa Question Video: Finding the Inverse of Linear Functions | Nagwa

Question Video: Finding the Inverse of Linear Functions Mathematics • Second Year of Secondary School

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What is the inverse of the function 𝑦 = 7π‘₯ βˆ’ 5?

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Video Transcript

What is the inverse of the function 𝑦 equals seven π‘₯ minus five?

First, let’s consider what an inverse is. Formally, we could say if 𝑦 equals 𝑓 of π‘₯, then π‘₯ equals the inverse function evaluated at 𝑦. What’s happening here is that we’re switching the input and the output. For the function 𝑓 of π‘₯, the input values are π‘₯ and the output values are 𝑦. For the inverse, the input values will be 𝑦 and the output values will be π‘₯.

There’s 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 𝑦. And in step two, we rearrange to express 𝑦 in terms of π‘₯. We know that 𝑦 equals seven π‘₯ minus five. But for our inverse function, π‘₯ is going to equal seven 𝑦 minus five. This completes step one.

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

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