Question

If f= {(7,2), (8,3), (12,4)} and g= {(2,7), (3,8), (6, 12)} write fog - 
1. {(2, 2), (3, 3), (6, 4)}
2. {(2, 2), (3, 3), (4, 4)}
3. {(3, 3), (6, 4)}
4. {(2, 7), (3, 8), (6, 12)}

Answer 1

Correct Answer - Option 1 : {(2, 2), (3, 3), (6, 4)}

CONCEPT:

Let f: A → B and g: B → C be two functions. Then, the composition of f and g, denoted by g o f, is defined as the function g o f: A → C given by g o f (x) = g (f (x)), ∀ x ∈ A.

CALCUATIONS:

f = {(7,2), (8,3), (12,4)} and g = {(2,7), (3,8), (6, 12)}

(fog)(x) = f(g(x))

f(g(2)) = f(7) = 2, (2,2) ∈ fog

f(g(3)) = f(8) = 3, (3,3) ∈ fog

f(g(6)) = f(12) = 4, (6,4) ∈ fog

So, fog = {(2,2), (3,3), (6,4)}.