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The range of the function \[\begin{aligned}f(x)=\log _{\sqrt{5}}\left(3+\cos \left(\frac{3 \pi}{4}\right.\right. & +x)+\…

Q1
PYQ

The range of the function
\[\begin{aligned}f(x)=\log _{\sqrt{5}}\left(3+\cos \left(\frac{3 \pi}{4}\right.\right. & +x)+\cos \left(\frac{\pi}{4}+x\right) \\& \left.+\cos \left(\frac{\pi}{4}-x\right)-\cos \left(\frac{3 \pi}{4}-x\right)\right)\end{aligned}\]

[JEE Main 2021, 1 Sep (Shift 2)]

a

\([-2,2]\)

b

\(\left[\frac{1}{\sqrt{5}}, \sqrt{5}\right]\)

c

\((0, \sqrt{5})\)

d

\([0,2]\)

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