Find the Domain ab

Problem

ƒ(x)=ln(x2−4)

Solution

1. Identify the restriction for the natural logarithm function, which requires the argument to be strictly greater than zero.

x2−4>0

2. Factor the quadratic expression using the difference of squares formula.

(x−2)*(x+2)>0

3. Determine the critical points by setting the factors equal to zero, which gives x=2 and x=−2

4. Test the intervals (−∞,−2) (−2,2) and (2,∞) to see where the inequality holds true.

• For x<−2 the product is positive.

• For −2<x<2 the product is negative.

• For x>2 the product is positive.

5. Conclude that the domain consists of the intervals where the expression is positive.

Final Answer

Domain:(−∞,−2)∪(2,∞)

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