Inverse Trigonometric Functions · Question 10

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

Answer

(3) 3

For -1(2x2 - 3x + 1): -1 2x2 - 3x + 1 1

Right part: 2x2 - 3x 0 x(2x - 3) 0 0 x 32

Left part: 2x2 - 3x + 2 0, true for all real x (discriminant 9 - 16 < 0).

For -1 ( 2x - 511 - 3x ): -1 2x - 511 - 3x 1

For 0 x 32, 11 - 3x > 0, so

-(11 - 3x) 2x - 5 11 - 3x

x 6 and x 165, both true for every x [0, 32 ].

Domain = [0, 32 ]

= 0, = 32

+ 2 = 0 + 3 = 3

Answer: (3)

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