Find the Domain f(x)=x/(x-2)

Problem

ƒ(x)=x/(x−2)

Solution

1. Identify the type of function. This is a rational function, which 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 of x

x−2=0

3. Solve for x by adding 2 to both sides of the equation.

x=2

4. Determine the domain by excluding the value that makes the denominator zero. The domain consists of all real numbers except x=2

5. Express the domain in interval notation.

(−∞,2)∪(2,∞)

Final Answer

Domain:(−∞,2)∪(2,∞)

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