# Multivariate function taking just one variable?

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Why in some books is there a multivariate function specifying just one variable when it is supposed to take two or more. For example:
why

f(x)= x²+y²

and not

f(x,y)=x²+y²

Should yield the corresponding value of z.

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It is common with a lot of mathematicians to use a different font/style to denote a tuple or vector, for example $$\mathbb x = (x, y)$$ and then define the function as $$f(\mathbb x) = f(x, y) = x^2 + y^2$$.

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