How do you find g o f which is g(f(x)) when f(x)=x^2-2 and g(x)=1/(x-2)?

1 Answer
Jun 6, 2016

It depends.

Explanation:

Technically, g circ f is not a well-defined function. This is because R_f = [–2,infty) is not a subset of D_g = RR excluding 2. In order for this function to be well defined, we restrict D_f to either (2, infty) or (–infty, –2), so that R_f = (2, infty) sube D_g

Now that g circ f is defined, we start with your statement, that is, g circ f = g(f(x)).

Then g(f(x))=g(x^2-2)=1/((x^2-2)-2)=1/(x^2-4).