JEE Main202313 Apr 2023Evening ShiftMathematicsFunctionsActual

The range of f x = 4 sin - 1 x 2 x 2 + 1 is

Options

A[ 0 , 2 π ]
B[ 0 , π ]
C[ 0 , 2 π )
D[ 0 , π )

Correct answer

C. [ 0 , 2 π )

Step-by-step solution

Given, f x = 4 sin - 1 x 2 x 2 + 1 Now taking, x 2 1 + x 2 = 1 - 1 1 + x 2 < 1 ⇒ 0 ≤ x 2 1 + x 2 < 1 Now taking sin - 1 we get, ⇒ 0 ≤ sin - 1 x 2 1 + x 2 < π 2 ⇒ 0 ≤ 4 sin - 1 x 2 1 + x 2 < 2 π Hence, the range of 4 sin - 1 x 2 x 2 + 1 is [ 0 , 2 π )

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