JAMIA 2022 — Mathematics PYQ

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Question

JAMIA 2022 — Mathematics PYQ

JAMIA | Mathematics | 2022

$The domain of ∣ x - 2∣ - 1 + 3 - ∣ x - 2∣ is$

Choose the correct answer:

Explanation

Step 1: Set up the conditions

For the square roots to be defined, we need:

$|x - 2| - 1 \ge 0$
$3 - |x - 2| \ge 0$

Step 2: Solve the first inequality

$|x - 2| - 1 \ge 0$

$|x - 2| \ge 1$

This implies:

$x - 2 \le -1$ or $x - 2 \ge 1$

$x \le 1$ or $x \ge 3$

In interval notation: $x \in (-\infty, 1] \cup [3, \infty)$

Step 3: Solve the second inequality

$3 - |x - 2| \ge 0$

$|x - 2| \le 3$

This implies:

$-3 \le x - 2 \le 3$

$-1 \le x \le 5$

In interval notation: $x \in [-1, 5]$

Step 4: Find the intersection

The domain is the intersection of the two solution sets:

$D = ((-\infty, 1] \cup [3, \infty)) \cap [-1, 5]$

Intersection of $(-\infty, 1]$ and $[-1, 5]$ is $[-1, 1]$ .
Intersection of $[3, \infty)$ and $[-1, 5]$ is $[3, 5]$ .

Combining these, we get:

$D = [-1, 1] \cup [3, 5]$

Final Answer:

The domain of the function is:

$[-1, 1] \cup [3, 5]$

Choose the correct answer:

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