Can someone explain how to do this? the question is in the picture.

For F(G(X)), plug in all of G(x) for the x values in F(x).  

That would look like:

F(G(x)) = ([(-3x-7)/(x-1)] - 7) / ([(-3x-7)/(x-1)] + 3)

multiply the -7 and the 3 by (x-1) so that both the numerator and denominator of the big fraction have denominators of (x-1).

both denominators cancel out then.

this becomes:

(-10x)/-10 => x

So the first one is true.  

 Follow the same steps for g(f(x)).  

Plug in all of (f(x)) for where g(x) has x's. then manipulate to get the answer x, if you do get just x, then both can be confirmed true.

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.