Hello

I believe this may be what you looking for?

Functions to be used later

exampleF1[u_, v_] := u Cos[v]

exampleF2[u_, v_] := ArcTan[u, v]

exampleG1[u_, v_] := (u + v) u

exampleG2[u_, v_] := (u - v) Exp[v]

Function to create your equation, and example usage

myEquation[f_, g_, q_, t_] := f[q, t] == g[1/t, 1/q]

myEquation[exampleF1, exampleG1, q, t]

myEquation[exampleF2, exampleG1, q, t]