Find the function of a)f*g b)g*f c)f*f d)g*g and their domains.

Question

f(x)=x/1+x g(x)=sin2x

Just the functions and domains.

I would appreciate it if the steps were also written out to how you got the answer because it would help me do it.

Answer 1

You just multiply the functions together and then look for issues that would prevent "x" from being any number:

I'm unsure whether g(x) = sin(2x) or if it is g(x) = sin²(x) but, I'll assume the first:

The domain restriction is that you cannot divide by zero so x cannot equal -1 meaning the domain is:

(-∞,-1)U(-1,∞)

Notice that b) is the exact same answer.

For c) you get x²/(1 + x)² and you have the same domain restrictions.

But for d) you get sin²(2x) and there are no restrictions for the domain so the domain is (-∞,-∞). Remember that the graph of y = sin(x) is continuous for all "x"