Question

Let A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and f, g: A → B be functions defined by F(x) = x² − x, x ∈ A and g(x)=2|x−1/2|−1,∈ A. Are f and g equal? Justify your answer. (Hint: One may note that two function f: A → B and g: A → B such that F(a) = g(a) ∀ a ∈ A, are called equal functions). 

Answer 1

(0)=(0)²−(0)=0
and g(0)=2|0−1/2|−1=2(1/2)−1=1−1=0 ⇒ f(0)=g(0)

f(1)=(1)²−(1)=1−1=0
and g(1)=2|(1)−1/2|−1=2(1/2)−1=1−1=0 ⇒ f(1)=g(1)

Hence, the functions f and are equal.