Find the Domain x/(x^2-16)

Problem

x/(x^2−16)

Solution

1. Identify the condition for the domain of a rational function. The function is defined for all real numbers except where the denominator is equal to zero.

2. Set the denominator equal to zero to find the excluded values.

x^2−16=0

3. Factor the difference of squares on the left side of the equation.

(x−4)*(x+4)=0

4. Solve for x by setting each factor to zero.

x−4=0⇒x=4

x+4=0⇒x=−4

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

Final Answer

Domain: *{x|x≠4,−4}

Want more problems? Check here!