<s>[INST] If $f(2x-3) = 4x-2$, then what is $f(x)$? I have this statement: 

If $f(2x-3) = 4x-2,$ the function $f(x)$ is ...?

My attempt was:
Move the function $3$ units to the left
$f(2x) = 4(x+3) -2 = 4x+10$
Divide $x$ by $2$
$f(x) = 2x+10$
Verifiy $f(x) = 2x+10 \to f(2x) = 4x+10 \to f(2x-3) = 4(x-3)+10 = \underbrace{4x-2}_{f(2x-3)}$
But according to the  guide the correct answer is $2x+4$ and i don't know why. Thans in advance.
 [/INST] If $x\in\mathbb R$, then\begin{align}f(x)&=f\left(2\frac x2\right)\\&=f\left(2\left(\frac x2+\frac32\right)-3\right)\\&=4\left(\frac x2+\frac32\right)-2\\&=2x+4.\end{align}
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