someone help me this is for an assignment and I've been having problems with this question

Given that f(x)=3x + 1 and g(x)=5x + k,find k if fg(x)=gf(x).and the last part to this question is check that a is correct by showing that fg(3)=gf(3) :rolleyes:

By fg(x) and gf(x), I assume you mean f(g(x)) and g(f(x))?

If so, it is a composite. Insert g into f and f into g, equate, and solve for k.

f(g(x))=3(5x+k)+1

g(f(x))=5(3x+1)+k

Now, set equal and find k.