Find the Domain g(x)=(3x)/(2x^2-4x)

Problem

g(x)=(3*x)/(2*x^2−4*x)

Solution

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

2*x^2−4*x≠0

2. Factor the expression in the denominator by taking out the greatest common factor.

2*x*(x−2)≠0

3. Solve for the values of x that make the denominator zero by setting each factor to zero.

2*x=0⇒x=0

x−2=0⇒x=2

4. Exclude these values from the set of all real numbers to define the domain.

Domain={x|x∈ℝ,x≠0,x≠2}

Final Answer

Domain of *g(x)=(−∞,0)∪(0,2)∪(2,∞)

Want more problems? Check here!