What is the conjugate of the conjugate of a function?

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Let $f$ be a convex function.

Then the conjugate of $f$ is defined as $f^*(y) \equiv \sup_{x}(y^Tx - f(x))$

How is the conjugate of the conjugate defined $f^{**}(y) \equiv ?$

Edit for question clarity:

Is it $f^{**} : Z \rightarrow \Bbb R$ by $f^{**}(z) = \sup_{y}(z^Ty - f^*(y))$? Is it $f^{**}(z) = \sup_{x}(z^Tx - f^*(y))$? Is the domain changed every time you take a conjugate or is $Z=Y$?