Find the Domain g(x)=x/(x^2-5x)

Problem

g(x)=x/(x2−5*x)

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≠0

2. Factor the expression in the denominator to find the values of x that must be excluded from the domain.

x*(x−5)≠0

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

x≠0

x−5≠0⇒x≠5

4. State the domain in interval notation, excluding the values 0 and 5 from the set of all real numbers.

(−∞,0)∪(0,5)∪(5,∞)

Final Answer

Domain of *g(x)=(−∞,0)∪(0,5)∪(5,∞)

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