The range of $f (x) = 6 sin x + 8 cos x + 3$ is

[6, 8]

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[6, 13]

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[- 7, 13]

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[3, 6]

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Solution

The correct option is C $[- 7, 13]$
$f (x) = 6 s i n x + 8 c o s x + 3$
Range of $A sin x + B cos x$ is $[- \sqrt{A^{2} + B^{2}}, \sqrt{A^{2} + B^{2}}]$
$- 10 ⩽ 6 sin x + 8 cos x ⩽ 10$
So, $- 10 + 3 ⩽ f (x) ⩽ 10 + 3$
$- 7 ⩽ f (x) ⩽ 13$

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