# Let a = {−2, −1, 0, 1, 2} And F : a → Z Be a Function Defined By F(X) = X2 − 2x − 3. Find:(B) Pre-images of 6, −3 and 5. - Mathematics

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

(b) pre-images of 6, −3 and 5.

#### Solution

(b) Let x be the pre-image of 6.
Then,
f(6) = x2 − 2x − 3 = 6
⇒ x2 − 2x − 9 = 0
⇒ $x = 1 \pm \sqrt{10}$

Since

$x = 1 \pm \sqrt{10} \not\in A$  there is no pre-image of 6.

Let x be the pre-image of -3. Then,
f(− 3) ⇒ x2 − 2x − 3 = − 3
⇒ x2 − 2x  = 0
x = 0, 2
Clearly
$0, 2 \in A$

So, 0 and 2 are pre-images of  −3.

Let x be the pre-image of  5. Then,
f(5) ⇒ x2 − 2x − 3 = 5
⇒ x2 − 2x − 8 = 0
⇒ (x − 4) (x + 2) = 0  ⇒ x = 4, − 2
Since

$- 2 \in A$  2 is the pre-image of 5.
Hence,
pre-images of 6, − 3 and 5 are  $\phi, \left\{ 0, 2, \right\}, - 2$ respectively.
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.1 | Q 4.2 | Page 7