Inverse Trigonometric Functions · Question 13

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Considering the principal values of the inverse trigonometric functions, -1 ( 32x + 12 1 - x2 ), - 12 < x < 1 2, is equal to

Answer

(3) 6 + -1x

Put x = , where = -1x.

- 12 < x < 1 2 - 6 < < 4, and 1 - x2 = (as > 0)

32x + 12 1 - x2 = 6 + 6

= ( + 6 )

Now 0 < + 6 < 5 12, which lies in [- 2, 2 ], so

-1 ( ( + 6 ) ) = + 6

= 6 + -1x

Answer: (3)

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