<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] Since the argument and output are linear, we can try to extract $2x-3$ from $4x-2$ through arithmetic means. 
\begin{align}
f(\color{red}{2x-3})&=4x-2\\
&=4x\color{blue}{-6+6}-2\\
&=2(\color{red}{2x-3})+4
\end{align} 
Therefore, $f(x)=2x+4$ as required. 
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