# In a function like f(x,y)=x^2+y, are x and y independent of each other and are we allowed to pick values for each deliberately?

In a function like $f\left(x,y\right)={x}^{2}+y$, are $x$ and $y$ independent of each other and are we allowed to pick values for each deliberately?
Say for $1$ for $x$ and $99$ for $y$?
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Finnegan Stone
In general
$f\left(x,y\right):D\subseteq {\mathbb{R}}^{\mathbb{2}}\to \mathbb{R}$
is defined in a subset $D$ of ${\mathbb{R}}^{\mathbb{2}}$ that is the real plane.
$f\left(x,y\right)={x}^{2}+y$
is defined for each value of $\left(x,y\right)$ thus $D\equiv {\mathbb{R}}^{\mathbb{2}}$.