CUET PG 2023 — Mathematics PYQ

Q: How do I solve CUET PG 2023 Mathematics questions?

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Question

CUET PG 2023 — Mathematics PYQ

CUET PG | Mathematics | 2023

If 𝑓 ∶ 𝑅 → 𝑅 defined as of 𝑓(𝑥) = x² + 1 then minimum value of 𝑓(𝑥) is

Choose the correct answer:

Explanation

Analyze the square term: For any real number $x$ , the square of the number is always non-negative. Therefore:

$x^{2} \ge 0$
Add the constant: Adding $1$ to both sides of the inequality:

$x^{2} + 1 \ge 0 + 1$

$f(x) \ge 1$
Determine the point of minimum: The smallest possible value for $x^{2}$ is $0$ , which occurs when $x = 0$ . Substituting $x = 0$ into the function:

$f(0) = 0^{2} + 1 = 1$

Conclusion:

The minimum value of $f(x)$ is $1$ .