Find the Domain y

Problem

y=(x−1)/(x2−4)

Solution

1. Identify the type of function, which is a rational function where the domain is restricted by the denominator.

2. Set the denominator equal to zero to find the values of x that are excluded from the domain because division by zero is undefined.

x2−4=0

3. Solve for x by factoring the difference of squares or by taking the square root of both sides.

x2=4

x=±2

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

x≠2

x≠−2

Final Answer

Domain: *(−∞,−2)∪(−2,2)∪(2,∞)

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