Representing a function in a different space

[Apteronotus]

I have an implicit function f(x,y,z) which represents a surface in the XYZ Cartesian reference frame. I would like to change this current XYZ reference frame by a matrix M.
ie.
$M: XYZ \rightarrow X'Y'Z'$

If I have a vector v in XYZ, then v'=Mv is my representation of v in the X'Y'Z' reference frame. But how do I get a representation of my function f in X'Y'Z'? Specially, as f is given in terms of (x,y,z) and cannot easily be solved for each of its components.

Thanks

 

[Petr Mugver]

f transforms as a scalar, that means (I put r = (x,y,z)):

f(r) = f '(r ')

and since r ' = Mr

$f'(r')=f(M^{-1}r')$

In other words $f'=f\circ M^{-1}$