If f : A → B defined as f x = 2 sin ⁡ x - 2 cos ⁡ x + 3 2 is an invertible function, then the correct statement can be

Question

If f : A → B defined as f x = 2 sin ⁡ x - 2 cos ⁡ x + 3 2 is an invertible function, then the correct statement can be, A = π 4 , 5 π 4 , B = 2 2 , 5 5, A = - π 4 , 5 π 4 , B = 2 , 5 2, A = - π 4 , 3 π 4 , B = 2 , 4 2, A = - π 4 , 3 π 4 , B = 2 , 5 2

MARKS App · Accepted Answer

f x = 2 2 1 2 sin ⁡ x - 1 2 cos ⁡ x + 3 2 = 2 2 sin ⁡ x - π 4 + 3 2 Clearly, for options A and B f x is not injective and for option C f x is not surjective f x is bijective only for option D

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