Hi! May you please explain how to find the function for f(x) for number 5 from the practice questions in the “functions” chapter? I saw the solution, which said to find f(5+3), and then I got the correct answer, but I wanted to see if there is a function that could be found (as I tried to find it but I found it incorrectly and got an incorrect answer).

Sure. Here’s the question for those following along:

As you note, the quick and dirty way to go is to set x=5 and solve for f(5+3). If you really want to find f(x), though, it can be done. Just think through everything that needs to happen to (x+3) to turn it into 10x+4!

First, it’s going to have to be multiplied by 10.

But 10(x+3)=10x+30, not 10x+4.

So after you multiply by 10, subtract 26! That will land you right where you want to be. 10(x+3)-26=10x+4, so the function is f(x)=10x-26.

Solve that for f(8):

f(x)=10x-26\\f(8)=10(8)-26\\f(8)=54

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