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

Question

The range of f x = 4 sin - 1 x 2 x 2 + 1 is, [ 0 , 2 π ], [ 0 , π ], [ 0 , 2 π ), [ 0 , π )

MARKS App · Accepted Answer

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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