A) \[\left[ \frac{\pi }{4},\frac{5\pi }{4} \right]\to [\sqrt{2},3\sqrt{2}]\]
B) \[\left[ -\frac{3\pi }{4},\frac{\pi }{4} \right]\to [\sqrt{2},3\sqrt{2}]\]
C) \[\left[ -\frac{3\pi }{4},\frac{3\pi }{4} \right]\to [\sqrt{2},3\sqrt{2}]\]
D) none of these
Correct Answer: C
Solution :
[c] \[f(x)=\sqrt{2}\sin \left( x+\frac{\pi }{4} \right)+2\sqrt{2}\] Or \[f(x)=\sqrt{2}\cos \left( x-\frac{\pi }{4} \right)+2\sqrt{2}\] i.e., \[Y=[\sqrt{2},3\sqrt{2}]\] and \[X=\left[ -\frac{3\pi }{4},\frac{\pi }{4} \right]\] or \[\left[ \frac{\pi }{4},\frac{5\pi }{4} \right]\]
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