Finding the formula of a function based on output This is probably something super simple, but I can't find it in my book, and I don't even know what to search for because I don't know what to call it.
I'm not looking for this specific answer, but how would I approach a problem like this.
$$ \mbox{If}\ f(x - 4) = 3x + 2,\ \mbox{find}\ f(-2).$$
So, $3x+2$ is the output, being modified by the formula I need to find. I don't know how to algebraically find that equation without brute forcing. For what it's worth, the answer above was apparently $-12$.
Edit. Answer was not -12, but still had trouble figuring out how to approach to find correct answer.
 A: Here are the steps in full detail
$$ f(x-4)=3x+2 $$
$$ \frac13 f(x-4)=x+\frac23 $$
$$ \frac13 f(x-4)=x+\frac23 +\frac13-\frac13 $$
$$ \frac13 f(x-4)=x+1-\frac13 $$
$$ \frac13 f(x-4)=x+1-5+5-\frac13 $$
$$ \frac13 f(x-4)=x-4+5-\frac13 $$
$$ f(x-4)=3(x-4)+15-1 $$
$$ f(x-4)=3(x-4)+14 $$
$$ f(s)=3s+14 $$
So now we have
$$ f(-2)=3(-2)+14 =-6+14=8$$
We can also skip all of this and just use the fact that
$$ x-4 =-2 $$
$$ x =-2 +4 =2 $$
So now we have
$$ f(2-4)=f(-2)=3(2)+2 $$
$$=6+2=8 $$
Either way,
$$f(-2)\not =-12$$
A: If you want $f(-2)$ and you know that $f(x-4)=3x+2$, then you want $x-4=-2$. Does that help? 
By the way, I think your supposed answer of $-12$ is incorrect.
A: There are two ways to look at your question.
1) you just want to compute $f(-2)$. For this, you need to find $x$ such that $x-4=-2$. Obviously, $x=2$ and $f(-2)=3\cdot2+2$.
$$f(-2)=8.$$
2) you want to get the expression for $f(x)$ instead of $f(x-4)$. In this case, use a change of variable $y=x-4$, hence $x=y+4$, and $f(y)=3x+2=3y+14$.
$$f(x)=3x+14.$$
