Find the Domain f(x)=3/(x^2-2x-15)

Problem

ƒ(x)=3/(x2−2*x−15)

Solution

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

x2−2*x−15≠0

2. Factor the quadratic expression in the denominator by finding two numbers that multiply to −15 and add to −2

(x−5)*(x+3)≠0

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

x−5=0⇒x=5

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≠5}

Final Answer

Domain:(−∞,−3)∪(−3,5)∪(5,∞)

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