Is it possible to write a function $f$ of the variable $x$ $f(x) = 2x$ in the following way? Imagine $u$ is a variable and $u = x + 3$. Can I write the function $f$ as $f(u - 3) = 2 \times (u - 3)$? I have seen this somewhere but I find it odd. For me, what's inside the brackets is the variable of the function, so I would write it like this: $f(u) = 2 \times (u - 3)$.
So $f(x = 1) = 2 \times 1 = 2$
$f(u = 4) = 2 \times (4 - 3) = 2$
Thanks. C.
If $x=u-3$ then you can replace $x$ by $u-3$, and vice-versa, anywhere that $x$ or $u-3$ appears, because they are the same thing . So if $x=u-3$ and $f(x)=2x$ then $$f(u-3)=f(x)=2x=2(u-3).$$ If $f(x)=2x$ for all possible values of $x,$ then $f($whatever$)=2($whatever). And if "whatever" happens to be $u-3$, you cannot change it to $u$ on the LHS of the equation.