If/(x) = 2x + 1, determine the function g(x) such that (f° g)(x) = x. Then use this function to determine (g of)(x).

Question

If/(x) = 2x + 1, determine the function g(x) such that (f° g)(x) = x. Then use this function to determine (g of)(x).

Answer 1

Given f(x) = 2x + 1

 

Now (f ° g)(x) = f(g(x)) = 2g(x) + 1 = x

 

Then g(x) = (x - 1)/2

 

(g o f)(x) = g(fx))

              = (f(x) - 1)/2

              = (2x + 1 - 1)/2

              = (2x)/2

             = x