Find the Domain h(x)=10/(x^2-2x)

Problem

h(x)=10/(x2−2*x)

Solution

1. Identify the restriction for a rational function, which is that the denominator cannot be equal to zero.

x2−2*x≠0

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

x*(x−2)≠0

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

x≠0

x−2≠0⇒x≠2

4. Express the domain in interval notation, excluding the points where the function is undefined.

(−∞,0)∪(0,2)∪(2,∞)

Final Answer

Domain of *h(x)=(−∞,0)∪(0,2)∪(2,∞)

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