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Find the range of f(x)=|sinx|+|cosx|, x ...

Find the range of `f(x)=|sinx|+|cosx|, x in R`.

Text Solution

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`f(x)=|sinx|+|cosx|, x in R`.
Clearly, `f(x) gt 0`.
Also, `f^(2)(x)=sin^(2)x+cos^(2)x+|2 sinx cos x|=1+|sin2x|`
Now, `0 le |sin zx|le1`
` :. 1 le 1 +|sin zx| le 2`
` :. 1 le f^(2)(x) le 2`
or ` 1 le f(x) le sqrt(2)`
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