<s>[INST] For $y = 2f\left(0.5x+4\right)-3$, derive the equation of: $ f(x)=2x^2-3x+4. $ 
For $y = 2f\left(0.5x+4\right)-3$,
derive the equation of:
$$
f(x)=2x^2-3x+4.
$$
I don't really understand what this question is asking for. Any input would be greatly appreciated.
 [/INST] I think that the (admittedly poorly worded) problem is asking for you to express $y$ in terms of $x$ given that $\displaystyle y=2\ f\left(\frac x 2 + 4\right)-3$ and $f(x)=2x^2-3x+4$.
In that case:
\begin{align}
y&=2\ f\left(\frac x 2 + 4\right) - 3\\
&=2\left(2\left(\frac x 2 + 4\right)^2 - 3 \left(\frac x 2 + 4\right)+4\right)-3\\
&=\dots
\end{align}
</s>