Question 28504: Find the Domain of the Rational Function
f(X)=X^2-4X-21/X^2+3X+2
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Thank You
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! f(x)=(x^2-4x-21)/(x^2+3x+2)
=[(x-7)(x+3)]/[(x+1)(x+2)] (factorising the nr and dr)
Since division by zero is not defined, the dr [(x+1)(x+2)] SHOULD NOT BE ZERO
And the dr will be zero for either (x+1) = 0 implying x = -1
or for (x+2) = 0 implying x = -2
Therefore x=-2 and x=-3 should not be domain members because if they are there in the domain set f(x) is not defined. That is we cannot find f- image for these two values of x
Therefore we conclude the domain of the given function is the set of all real numbers excepting the values -1 and -2
That is the domain set is the complement of the set {-1,-2} in the real number system R
That is the required domain set is R - {-1,-2}
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