the algebra on this gets very messy haha, but basically you want to plug in each function and then simplify it down algebraically to prove that it is equal to x!
f(g(x)) = [(-3x - 7) / (x - 1) - 7] / [(-3x - 7)/(x-1) + 3)] = (-10x / x - 1) / (-10 / x - 1) = -10x/-10 = x
g(f(x)) = [-3(x - 7) / (x - 3) - 7] / [(x - 7) / (x + 3) - 1] = (-10x / x + 3) / (-10 / x + 3) = -10x / -10 = x
so since both conditions are met that means that they are inverses of each other! :)
