Question: How to pass arguments of numeric type to a Spline function - when plotting

First a little background: I am using Maple 14 on a Windows 64 bit machine.

I first imported some x,y data using the readdata function. Then I made a Spline function from this data like so: f :=x->Spline(data,x);

Then I created a second function, lets call it g(z) which calls f like so: g:=z->f(1/z);

If I simply try to evaluate g(z) at a point it works. But if I try to plot g(z), like so: plot(g(z), z=5..7) I get the error: Error, (in CurveFitting:-Spline) 2nd argument must have type name or numeric

I understand that the initial Spline function f(x) needs a numeric type value passed to it. But I don't understand why g(z) works when you simply evaluate it at a point but doesn't work when you try to plot if over a range of values.

I have attached the relevant files. Any help is most appreciated.