Find the Domain f(x)=(x+4)/(x^2-9)

Problem

ƒ(x)=(x+4)/(x2−9)

Solution

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

x2−9≠0

2. Factor the denominator using the difference of squares formula, a2−b2=(a−b)*(a+b)

(x−3)*(x+3)≠0

3. Solve for the excluded values by setting each factor to zero.

x−3=0⇒x=3

x+3=0⇒x=−3

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

Domain={x|x∈ℝ,x≠3,x≠−3}

Final Answer

Domain=(−∞,−3)∪(−3,3)∪(3,∞)

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