I try to make the inverse of a one to one piecewise function, but the solve command gives a function of lists. How can I avoid this?

restart;
f := x -> piecewise( x<=1, (x-1)/2, x<2, -3*(x-1)+3, 2*(x-2)+3 ):
solve( f(x)=y, x ): g := unapply(%,y): lprint(g(x));
piecewise(x <= 0, [1+2*x], x < 3, [2-(1/3)*x], 3 <= x, [1/2+(1/2)*x])

An implicitplot3d of an f(x,y,z)=0 results in an ISOSURFACE structure containing the samples of a function taken over a regular grid in 3-D space and is rendered as a 3-D surface approximating the zero surface of the function.
When I select the points with values of f(x,y,z) "close" to zero, I only get a few points on the surface:

restart;
q := plots:-implicitplot3d( x^2+y^3+z^4=1 ,x=-1..1,y=-1..1,z=-1..1, 
    style=wireframe, color=black ):
pdata := plottools:-getdata(q); # doesn't work...