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)#.