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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). - Mathematics

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).

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Solution

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

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.1 | Q 4.1 | Page 7
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