Find the Domain e=(x-2)/(xx-9)

Problem

e=(x−2)/(x2−9)

Solution

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

2. Set the denominator expression equal to zero to find the excluded values of x

x2−9=0

3. Solve the quadratic equation by factoring the difference of squares.

(x−3)*(x+3)=0

4. Determine the specific values of x that make the denominator zero by setting each factor to zero.

x−3=0⇒x=3

x+3=0⇒x=−3

5. State the domain as all real numbers except for the excluded values found in the previous step.

Final Answer

Domain: *{[x∈ℝ,x≠3,x≠−3]}

Want more problems? Check here!