p(y)=x^3-5 intersecting x axis

Question

In how many points does the graph of polynomial $$p(y) =x^3-5$$ meets the x-axis? It is $p(y)$ and not $p(x)$. so I am doubtful. Will this equation intersect x-axis at all? or is this invalid?

Answer 1

$$p(y) =x^3-5$$ does not make sense unless $P(y)$ is defined first.

If the independent variable is y, then why it is defined as a function of x ?

If $P(y)$ is a polynomial in $y$ then it should have been defined.

For example if $$p(y) =y^2+1 $$ then $$ y^2+1 =x^3-5$$ is an equation to be solved for $y=0$ to find x-intercepts.