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

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0,π2

−π4,π4

−π2,π2

[0,π]

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Correct option is B

fx= sinx+cosx , gx=x2-1 gfx=gsinx +cosx=sinx +cosx2-1 =1 +2sinx·cosx -1=sin2x sin 2x is invertible if 2x∈-π2,π2 ⇒x∈-π4,π4

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If f(x)=sin⁡x+cos⁡x,g(x)=x2−1, then g(f(x)) is invertible in the domain

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