Question

If $g\left(x\right)=\frac{x^3-ax}{4}$ and $g\left(2\right)=\frac{1}{2}$, what is the value of $g\left(4\right)$?

Answer 1

$g\left(2\right)=\frac{1}{2}$ and $g\left(2\right)=\frac{{\left(2\right)}^2-a\left(2\right)}{4}$
$\Rightarrow 8-2a=2$

$\Rightarrow 2a=6$

$\Rightarrow a=3$

$\Rightarrow g\left(x\right)=\frac{x^3-3x}{4}$

$g\left(4\right)=\frac{{\left(4\right)}^3-3\left(4\right)}{4}=\frac{4(4^2-3(1\left)\right)}{4}=\frac{16-3}{1}=13$