Let (a, b) be the coordinates of any point on the graph of y = g(x). The transformation of this point onto the graph of y = f(x) can be represented by the general form of a transformation, which is:
y = A*f(B(x-h))+k
where A, B, h, and k are constants representing the vertical stretch/compression, horizontal stretch/compression, horizontal shift, and vertical shift, respectively.
We can write this transformation in terms of the function g as follows:
y = A*g(B(x-h))+k
Therefore, the formula for the function f in terms of the function g is:
f(x) = A*g(B(x-h))+k
where A, B, h, and k are constants representing the transformation of the graph of y = g(x) onto the graph of y = f(x).