The possible values of 1-x2-3 lie in the interval

The correct option is B We know that x^2≥ 0 ∀ x ∈ R ⇒ x^2 + 3 ≥ 3; ∀ x ∈ R 3 ≤ x^2 + 3 lt; ∞ ⇒1/3≥1/x^2 + 3 gt; 1/∞ ⇒ 0 lt; 1/x^2 + 3≤1/3 So, the poss ...

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Standard XII

Mathematics

Law of Reciprocal

The possible ...

Question

The possible values of $\frac{1}{x^{2} + 3}$ lie in the interval

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Solution

The correct option is C

We know that $x^{2} \geq 0 \forall x \in R$

$\Rightarrow x^{2} + 3 \geq 3; \forall x \in R$

$3 \leq x^{2} + 3 < \infty$

$\Rightarrow \frac{1}{3} \geq \frac{1}{x^{2} + 3} > \frac{1}{\infty}$

$\Rightarrow 0 < \frac{1}{x^{2} + 3} \leq \frac{1}{3}$

So, the possible values of $\frac{1}{x^{2} + 3}$ lie in the interval $(0, \frac{1}{3}]$

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The possible values of 1x2+3 lie in the interval

The correct option is C We know that x2≥0∀x∈R ⇒x2+3≥3;∀x∈R 3≤x2+3<∞ ⇒13≥1x2+3>1∞ ⇒0<1x2+3≤13 So, the possible values of 1x2+3 lie in the interval (0,13]

The possible values of $\frac{1}{x^{2} + 3}$ lie in the interval