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Question

Find the domain of f(x) = 12x2+5x+2

A
R
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B
(2,12)
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C
(,2][2,)
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D
(,2][12,)
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Solution

The correct option is B (,2][12,)
The function will have a real value only when denominator which is under a square root is >0
=>2x2+5x+2>0
=>2x2+4x+x+2>0
=>2x(x+2)+1(x+2)>0
=>(2x+1)(x+2)>0
Case 1 when both (2x+1)(x+2)>0
=>x>12;or>2

=>x>12or(12,)
Case 2 when both (2x+1)(x+2)<0
=>x<12;or<2
=>x<2or(,2)

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