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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

f(x)=sin⁡x+cos⁡x,g(x)=x2−1 or g(f(x))=(sin⁡x+cos⁡x)2−1=sin⁡2xClearly, g(f (x)) is invertible in−π2≤2x≤π2('.' sin2x is invertible when -π2≤2x≤π2 or −π4≤x≤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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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