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Find the range of f(x)=(log)2((sinx-cos...

Find the range of `f(x)=(log)_2((sinx-cosx+3sqrt(2))/(sqrt(2)))`

Text Solution

Verified by Experts

The correct Answer is:
`[1,2]`
` -sqrt(2) le sinx - cos x le sqrt(2)`
or `2 sqrt(2) le sinx - cosx +3sqrt(2) le 4 sqrt(2)`
or `2 le (sinx - cos x + 3 sqrt(2))/(sqrt(2)) le 4`
or `log_(2)2 le log_(2)((sinx - cos x + 3 sqrt(2))/(sqrt(2))) le log_(2)4`
or `1 le log_(2)((sinx - cos x + 3 sqrt(2))/(sqrt(2))) le 2`
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