Relations Question 16
Question: Let $ f :X\to y,f(x)=sinx+cosx+2\sqrt{2} $ be invertible. Then which $ X\to Y $ is not possible?
Options:
A) $ [ \frac{\pi }{4},\frac{5\pi }{4} ]\to [\sqrt{2},3\sqrt{2}] $
B) $ [ -\frac{3\pi }{4},\frac{\pi }{4} ]\to [\sqrt{2},3\sqrt{2}] $
C) $ [ -\frac{3\pi }{4},\frac{3\pi }{4} ]\to [\sqrt{2},3\sqrt{2}] $
D) none of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)=\sqrt{2}\sin ( x+\frac{\pi }{4} )+2\sqrt{2} $
Or $ f(x)=\sqrt{2}\cos ( x-\frac{\pi }{4} )+2\sqrt{2} $
i.e., $ Y=[\sqrt{2},3\sqrt{2}] $ and $ X=[ -\frac{3\pi }{4},\frac{\pi }{4} ] $ or $ [ \frac{\pi }{4},\frac{5\pi }{4} ] $
BETA
