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Inverse Trigonometric Functions

Question
CBSEENMA12036255

If f : R S, defined by straight f left parenthesis straight x right parenthesis space equals space sin space straight x space minus space square root of 3 space cos space straight x space plus 1 , is onto, then the interval of S is

  • [0, 3]

  • [-1, 1]

  • [0, 1]

  • [-1, 3]

Solution

D.

[-1, 3]

since space minus 2 less or equal than space sin space straight x space minus square root of 3 space cos space straight x less or equal than 2
space minus 1 less or equal than space sin space straight x space minus square root of 3 space cos space straight x space plus space 1 space less or equal than space 3
Range space of space straight f left parenthesis straight x right parenthesis space equals space left square bracket negative 1 comma space 3 right square bracket

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