Let $f(x) = \sin 2x + \cos 2x$ and $g(x) = x^2 - 1$, then $g(f(x))$ is invertible in the domain

Question

$x \in \left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$

$x \in \left[0, \frac{\pi}{4}\right]$

$x \in \left[\frac{-\pi}{4}, \frac{\pi}{4}\right]$

$x \in \left[\frac{-\pi}{8}, \frac{\pi}{8}\right]$

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