Find the Domain -3/(x^2-5x-3)

Problem

ƒ(x)=(−3)/(x2−5*x−3)

Solution

1. Identify the condition for the domain of a rational function, which requires that the denominator cannot be equal to zero.

x2−5*x−3≠0

2. Apply the quadratic formula to find the values of x that make the denominator zero, using a=1 b=−5 and c=−3

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values into the formula.

x=(−(−5)±√(,(−5)2−4*(1)*(−3)))/(2*(1))

4. Simplify the expression under the radical and the denominator.

x=(5±√(,25+12))/2

x=(5±√(,37))/2

5. State the domain by excluding these two values from the set of all real numbers.

Domain={[x∈ℝ,x≠(5−√(,37))/2,x≠(5+√(,37))/2]}

Final Answer

Domain=(−∞,(5−√(,37))/2)∪((5−√(,37))/2,(5+√(,37))/2)∪((5+√(,37))/2,∞)

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