Let me start you off:
Also, I can work through it but I'm confused as how I would end up with one side with an X as the way I go through it I end up canceling the x's. Could you possibly go through it to the point where I wont have to cross out the X and end up with the same answer (0)?
Oops! I made a mistake on my original post. Th question is:
I'm a little confused as to how I would prove x=0 and without eliminating the x.
(The x+1 was not meant to be squarerooted)
I note that if x= 1, then F(1)= 1+ 1= 2 so G(F(1))= G(2)= 2+ 1= 3 while G(1)= 1+ 1= 2 so F(G(1))= F(2)= so you must mean "solve G(F(x))= F(G(x)) for x".
You have already been told that G(F(x))= and that F(G(x))= so you need to solve
That involves two square roots so you will need to square twice. First, say, subtract 1 from both sides to isolate the :
Now square both sides to get
can you finish that? Square again get rid of this second square root.
The final equation will have two solutions but only one of them satisfies the original equation. That happens when you square both sides of an equation or mutliply both sides of an equation by the same thing. For example, x= 2 has only one root but has two.