Inverse Trigonometric Functions · Question 16

Let S = \x : -1x = + -1x + -1(2x + 1) \. Then x S(2x - 1)2 is equal to .

Answer

5

Solution

Domain: -1 x 1 and -1 2x + 1 1 -1 x 0

-1x = 2 - -1x

2 - -1x = + -1x + -1(2x + 1)

-1(2x + 1) = - 2 - 2 -1x

Let -1x = [- 2, 0 ]; then - 2 - 2 [- 2, 2 ], so taking sine is valid:

2x + 1 = (- 2 - 2 ) = - 2 = -(1 - 2x2)

2x2 - 2x - 2 = 0 x2 - x - 1 = 0

x = 1 52

Only x = 1 - 52 lies in [-1, 0] S = \ 1 - 52 \

(2x - 1)2 = (1 - 5 - 1)2 = 5

Answer: 5