- Let `f : A → B` and `g : B → C` be two functions. Then the composition of `f` and `g`, denoted by `gof`, is defined as the function gof `: A → C` given by gof `(x) = g(f (x)), ∀ x ∈ A`.
E.g. : Let `f : {2, 3, 4, 5} → {3, 4, 5, 9}` and `g : {3, 4, 5, 9} → {7, 11, 15}` be functions defined as `f (2) = 3, f (3) = 4, f(4) = f (5) = 5` and `g (3) = g (4) = 7` and `g (5) = g (9) = 11`. Find `gof`.
Solution: We have `gof (2) = g (f (2)) = g (3) = 7, gof (3) = g (f (3)) = g (4) = 7, gof (4) = g (f (4)) = g (5) = 11` and `gof (5) = g (5) = 11`.
- Let `f : A → B` and `g : B → C` be two functions. Then the composition of `f` and `g`, denoted by `gof`, is defined as the function gof `: A → C` given by gof `(x) = g(f (x)), ∀ x ∈ A`.
E.g. : Let `f : {2, 3, 4, 5} → {3, 4, 5, 9}` and `g : {3, 4, 5, 9} → {7, 11, 15}` be functions defined as `f (2) = 3, f (3) = 4, f(4) = f (5) = 5` and `g (3) = g (4) = 7` and `g (5) = g (9) = 11`. Find `gof`.
Solution: We have `gof (2) = g (f (2)) = g (3) = 7, gof (3) = g (f (3)) = g (4) = 7, gof (4) = g (f (4)) = g (5) = 11` and `gof (5) = g (5) = 11`.