The values of x 2 for x -3 is a set of real numbers-A- positiveB- negativeC- non-positiveD- non-negative

The correct option is D non negativex gt; 3 x nbsp;∈ ( 3, ∞) ⇒ x nbsp;∈ ( 3,0) ∪ [0,∞) x nbsp;∈ ( 3,0) ⇒ x^2∈ (0,9) x nbsp;∈ [0,∞) ⇒ x^2∈ nbsp;[0, ...

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Byju's Answer

Standard XI

Mathematics

Squaring an Inequality

The values of...

Question

The values of $x^{2}$ for $x > - 3$ is a set of real numbers.

positive

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negative

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non-positive

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non-negative

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Solution

The correct option is D non-negative
x > -3

$x \in (- 3, \infty)$

$\Rightarrow x \in (- 3, 0) \cup [0, \infty)$

$x \in (- 3, 0) \Rightarrow x^{2} \in (0, 9)$

$x \in [0, \infty) \Rightarrow x^{2} \in [0, \infty)$

So,
$x^{2} \in (0, 9) \cup [0, \infty) \Rightarrow x^{2} \in [0, \infty)$

So, the values of $x^{2}$ is set of all non-negative real numbers.

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The values of x2 for x>−3 is a set of real numbers.

The correct option is D non-negativex > -3 x∈(−3,∞) ⇒x∈(−3,0)∪[0,∞) x∈(−3,0)⇒x2∈(0,9) x∈[0,∞)⇒x2∈[0,∞) So, x2∈(0,9)∪[0,∞)⇒x2∈[0,∞) So, the values of x2 is set of all non-negative real numbers.

The values of $x^{2}$ for $x > - 3$ is a set of real numbers.