Y is inversely proportional to the cube of x. This can be written as:
[tex]Y=\frac{k}{x^3}[/tex]
Where k is the constant of proportionality.
We know Y = 8 when x = 2. Substituting:
[tex]\begin{gathered} 8=\frac{k}{2^3} \\ \\ 8=\frac{k}{8} \\ \\ k=64 \end{gathered}[/tex]
Thus, the relationship is:
[tex]Y=\frac{64}{x^3}[/tex]
When x = 4, calculate Y:
[tex]Y=\frac{64}{4^3}=\frac{64}{64}=1[/tex]
When x = 4, Y = 1, thus the statement is false
