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Question

The set of all points of discontinuity of f(x)=x1x3+6x2+11x+6 is

A
ϕ
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B
{1}
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C
{1,2,3}
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D
{1,2,3}
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Solution

The correct option is C {1,2,3}
The denominator of the equation is given by
x3+6x2+11x+6=x3+6x2+9x+2x+6
=x(x2+6x+9)+2(x+3)
=x(x+3)2+2(x+3)
=(x+3)[x(x+3)+2]
=(x+3)(x2+3x+2)
=(x+3)(x+1)(x+2)
Thus f(x) =(x1)/(x+3)(x+1)(x+2)
Hence, f(x) is discontinuous at x=1,2,3

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