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Range of Trigonometric Expressions

The range of ...

Question

The range of the function $2 sin x + 7$ is

[0, 7]

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[- 7, 7]

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[5, 7]

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[5, 9]

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Solution

The correct option is D $[5, 9]$
We know $- 1 \leq sin x \leq 1$
$\Rightarrow - 2 \leq 2 sin x \leq 2$
$\Rightarrow 5 \leq 2 sin x + 7 \leq 9$
$∴$ Range $= [5, 9]$

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