<s>[INST] If $f(x-3) = x^2$, $f(x) = (x+3)^2$? I was wondering suppose you have $f(x-3) = x^2$. Is it correct to say that $f(x) = f(x-3 +3 ) = (x+3)^2$. If so, why or why not? Why can we say that if $g(x) = x^2 + x$, then $g(x+2) = (x+2)^2 + (x+2)$ but not the other way around?
 [/INST] I would interpret 
$f(x-3) = x^2$
as composition
$f \circ u$
where $u(x) = x - 3$. 
In this case $x = u + 3$ and $f(u) = x^2 = (u+3)^2$ or $f(x) = (x + 3)^2$.
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