Let A = {–2, –1, 0, 2} and f : A → Z: f(x) = x2 – 2x – 3. Find f(A).
Given :
A = {–2, –1, 0, 2}
f : A → Z: f(x) = x2 – 2x – 3
Finding f(x) for each value of x,
f(-2) = (-2)2 – 2(-2) – 3 = 4 + 4 -3 = 5
f(-1) = (-1)2 – 2(-1) – 3 = 1 + 2 -3 = 0
f(0) = (0)2 – 2(0) – 3 = 0 + 0 -3 = -3
f(2) = (2)2 – 2(2) – 3 = 4 - 4 -3 = -3
f in ordered pair is represented as
f = {(-2,5),(-1,0),(0,-3),(2,-3)}