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

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)]