If and , then is invertible in the…

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

If f(x)=sin⁡x+cos⁡xf(x)=\sin x+\cos x and g(x)=x2−1g(x)=x^2-1, then g{f(x)}g\{f(x)\} is invertible in the domain (1) [0,π2]\left[0,\frac{\pi}{2}\right] (2) [−π4,π4]\left[-\frac{\pi}{4},\frac{\pi}{4}\right] (3) [−π2,π2]\left[-\frac{\pi}{2},\frac{\pi}{2}\right] (4) [0,π][0,\pi]

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