Question

If $f\left(x\right)=(12x{)}^{3/2}$, and $n=f\left(3\right)$, what is the value of 2n?

Answer 1

Since we are given that $f\left(3\right)=n$, therefore, we substitute $x=3$ in $f\left(x\right)={\left(12x\right)}^{\frac{3}{2}}$ as shown below:

$f\left(x\right)={\left(12x\right)}^{\frac{3}{2}}\Rightarrow f\left(3\right)={(12\times 3)}^{\frac{3}{2}}\Rightarrow n={\left(36\right)}^{\frac{3}{2}}\Rightarrow n={\left(6^2\right)}^{\frac{3}{2}}\Rightarrow n=6^3\Rightarrow n=216$

Therefore, $n=216$ and $2n=2\times 216=432$.

Hence, $2n=432$.