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Squaring an Inequality

If x ∈[-4,3],...

Question

If $x \in [- 4, 3]$ , then $x^{2}$ lies in

A

[9, 16]

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B

[0, 9]

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C

[0, 16]

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D

[- 16, 9]

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Solution

The correct option is C $[0, 16]$
$x \in [- 4, 3]$
$\Rightarrow - 4 \leq x \leq 3$
$I$ .
$- 4 \leq x \leq 0$
$\Rightarrow 0 \leq x^{2} \leq 16$
$II$ .
$0 \leq x \leq 3$
$\Rightarrow 0 \leq x^{2} \leq 9$
$∴ 0 \leq x^{2} \leq 16$

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Squaring an Inequality

Standard XII Mathematics

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