For exercise a), f and g are the same function. So,
[tex] f(g(x)) = g(f(x)) = f(f(x)) = f\left(\dfrac{2}{x}\right) = \dfrac{2}{\frac{2}{x}} = x [/tex]
This means that f and g are inverse (i.e., f is the inverse of itself). In fact, if f(g(x)) = g(f(x)) = x, then f and g are inverse.
As for exercise b), you have
[tex] f(g(x)) = f(6x-1) = 6(6x-1)+1 = 36x-6+1 = 36x-5 [/tex]
[tex] g(f(x)) = g(6x+1) = 6(6x+1)-1 = 36x+6-1 = 36x+5 [/tex]
So, f and g are not inverse of each other.
