Inverse Trigonometric Functions

If k = ( 4 + 12 -1 ( 23 ) ) + ( 12 -1 ( 23 ) ), then the number of solutions of the equation -1(kx - 1) = -1x - -1x is .

Considering the principal values of inverse trigonometric functions, the value of the expression (2 -1 ( 2 13 ) - 2 -1 ( 3 10 ) ) is equal to :

1. 3356
2. - 3356
3. - 1663
4. 1663

If the domain of the function f(x) = -1 ( 1x2 - 2x - 2 ) is (- , ] [ , ] [ , ), then + + + is equal to

1. 4
2. 2
3. 5
4. 3

The number of solutions of -1 4x + -1 6x = 6, where - 12 6 < x < 12 6, is equal to :

1. 2
2. 0
3. 3
4. 1

If the domain of the function f(x) = -1 ( 2x - 511 - 3x ) + -1(2x2 - 3x + 1) is the interval [ , ], then + 2 is equal to :

1. 5
2. 2
3. 3
4. 1

Let the maximum value of ( -1x )2 + ( -1x )2 for x [- 32, 1 2 ] be mn 2, where (m, n) = 1. Then m + n is equal to .

The value of -1 ( 1+ 2(2)-1 (2) ) - -1 ( 1+ 2 ( 12 )+1 ( 12 ) ) is equal to

1. - 32
2. + 52
3. - 54
4. + 32

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

1. -5 6 - -1x
2. 5 6 - -1x
3. 6 + -1x
4. 4 + -1x

The sum of the infinite series -1 ( 74 )+ -1 ( 194 )+ -1 ( 394 )+ -1 ( 674 )+ is :

1. 2+ -1 ( 12 )
2. 2- -1 ( 12 )
3. 2- -1 ( 12 )
4. 2+ -1 ( 12 )

If y = ( 3 + -1 x2 ), then (x - y)2 + 3y2 is equal to .