<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] Let $y$ equal to an expression that will make $2y-3=x$ so that we can have $f(x)$.
This can be done if $y=\frac{x}{2}+1.5$
Plug $y$ in:
$f(2y-3)=4y-2$ and substitute the value of $y$ in terms of $x$:
$f(2(\frac{x}{2}+1.5)-3)=f(x)=4(\frac{x}{2}+1.5)-2=2x+4$
</s>