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Question

If f:RS defined by
f(x)=4sinx3cosx+1 is onto, then S is equal to

A
[5,5]
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B
(5,5)
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C
(4,6)
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D
[4,6]
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Solution

The correct option is D [4,6]
We have f(x)=4sinx3cosx+1

Therefore
maximum of f=42+(3)2+1=16+9+1=25+1=5+1=6 and
minimum of f=42+(3)2+1=16+9+1=25+1=5+1=4

S= Range of f=[minimumf,maximumf]=[4,6]

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