Find the Domain x-9/x-1

Problem

(x−9)/(x−1)

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 values that must be excluded from the domain.

x−1=0

3. Solve for x by adding 1 to both sides of the equation.

x=1

4. Determine the domain by excluding the value found in the previous step. The domain consists of all real numbers except x=1

5. Express the domain in interval notation.

(−∞,1)∪(1,∞)

Final Answer

Domain={x|x≠1}

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