Question

Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x² − 2x − 3. Find:

(a) range of f, i.e. f(A).

Answer 1

(a) Given:
f (x) = x² − 2x − 3
f (−2) = (− 2)² − 2(− 2) − 3
          = 4 + 4 – 3
          = 8 − 3 = 5
f (−1) = (−1)² − 2(−1) − 3
          = 1+ 2 − 3
          = 3 − 3 = 0
f (0) = (0)² − 2(0) − 3
        = 0 − 0 − 3
        = − 3
f (1) = (1)² − 2(1) − 3
        = 1 − 2 − 3
        =1 − 5 = − 4
f (2) = (2)² – 2(2) − 3
        = 4 − 4 – 3
        = 4 – 7 = − 3
Thus, range of f(A) = (− 4, − 3, 0, 5).