Question

Questions on picture

Answer 1

For exercise a), f and g are the same function. So,

`f(g(x)) = g(f(x)) = f(f(x)) = f\left((2)/(x)\right) = (2)/((2)/(x)) = x`

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

`f(g(x)) = f(6x-1) = 6(6x-1)+1 = 36x-6+1 = 36x-5`

`g(f(x)) = g(6x+1) = 6(6x+1)-1 = 36x+6-1 = 36x+5`

So, f and g are not inverse of each other.