So basically you say sub f(x) into g(x), replacing the xs in g(x) by f(x). For inverse you say y=g(x). You then rearrange to make x the subject. Then you just rewrite the x into g^-1(x) and the ys into xs. Is this further maths gcse? I honestly knew nothing about this topic until I started a2 maths this year but it's fairly simple once you've got your head around it and someone shows you how works. The inverse function basically works so that if you input A and got B from a function, if you input B into the inverse you would get A. The inverse function is also a reflection of the function in the line y=x.