NTA Abhyas JEE Main2020MathematicsFunctionsPractice

If f : A → B defined by f x = s i n x - c o s x + 3 2 is an invertible function, then the correct statement can be

Options

AA = π 4 , 5 π 4 , B = 3 2 , 4 2
BA = - π 4 , 5 π 4 , B = 2 2 , 4 2
CA = - π 4 , 3 π 4 , B = 2 , 4 2
DA = - π 4 , 3 π 4 , B = 2 2 , 4 2

Correct answer

D. A = - π 4 , 3 π 4 , B = 2 2 , 4 2

Step-by-step solution

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

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