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Question

Find the domain of the following function.
f(x)=x2+x6x24

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Solution

f(x)=x2+x6x24
(x2+x6)0
(x24)0
x2,2
x2+x60
x2+3x2x60
x(x+3)2(x+3)0
x=2,x=3
When, x>2
x2+x6<0
When, x<3
x2+x6<0
x=2 is not possible.
So, the domain of f(x)=(α,3](2,)

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