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If the domain of the function f(x) = -1 ( x - 12x + 3 ) is R - ( , ), then 12 is equal to :
(4) 32
-1u is defined for -1 u 1, so we need | x - 12x + 3 | 1, i.e. |x - 1| |2x + 3| with x - 32
Squaring: (2x + 3)2 - (x - 1)2 0
3x2 + 14x + 8 0 (x + 4)(3x + 2) 0
[figure]
So x -4 or x - 23 (the point - 32 already lies in the gap), hence domain = R - (-4, - 23 )
= -4, = - 23 and 12 = 12 83 = 32
Answer: (4)
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