For f(x)=3x+1 and g(x)=x^2-6 find (fog)(x)

Question

 Need help with the question. Not sure what to do. Also the minus 6 is not with the exponent.

Answer 1

Observe that (fog)(x) is equivalent to f(g(x)) which is to say intuitively the output of the function g(x) is fed as an input into the function f(x).

So in this case the general output of g(x) is x^2-6 for every input x. Thus fed as an input of f(x) in the form f(x^2-6) becomes 3(x^2-6)+1=3x^2-17.