Topic A: Functions
We're told that the formula for converting a Celsius temperature into Fahrenheit is the Celsius temperature, or C, is equal to 5/9 times the Fahrenheit temperature minus 32. Rewrite the formula so it solves for Fahrenheit. So just like I mentioned, the C is Celsius, is the Celsius temperature. And the F is the Fahrenheit temperature. So right now, it's expressed in terms of, we've solved for C in terms of F. Now we want to solve for F in terms of C. So let's see how we're going to do that. So I'll just rewrite it. C is equal to 5/9 times F minus 32. And we want to solve for F. So the first useful thing to do might be to get rid of this 5/9 from both sides, or at least from the right side of the equation, so we just have an F minus 32. And the easiest way to do that is to multiply by the inverse of 5/9. So if we multiply both sides of this equation by 9/5-- and I could put it here, but it'll squeeze a little tight, let me try it-- 9/5 in there. If I do it to the right-hand side of the equation, I also have to do it to the left-hand side of the equation. And what do I get? The left-hand side becomes 9/5 Celsius, or the Celsius temperature, 9/5 times the Celsius temperature, is equal to-- the whole reason we wanted to multiply the right side by 9/5 is these 9's cancel out, this 5 cancels out, and this just becomes a 1. So 9/5 times the Celsius temperature is going to be equal to this expression: the Fahrenheit temperature minus 32. We don't need the parentheses anymore, because this is the only expression on the right-hand side. Now, we want to solve for the Fahrenheit temperature. So let's see if we can get rid of this 32 from the right-hand side. The easiest way I know how to do that is to add 32. Add 32 to both sides of this equation. Add 32 to both sides. The left-hand side now becomes 9/5 times the Celsius temperature, plus 32. And that's going to be equal to-- this negative 32 and positive 32 cancel out, that was the whole point behind adding 32, so it's just going to be equal to F. And we're done. We have rewritten this formula, up here, so it solves for Fahrenheit. This is the Fahrenheit right here. We've solved for Fahrenheit in terms of the Celsius temperature.