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Domain of One Variable Function – A function with log – Exercise 5744

Exercise

Determine the domain of the function:

y=\log_a (x+2)+\log_a (x-2)

Final Answer


x>2

Solution

Let’s find the domain of the function:

y=\log_a (x+2)+\log_a (x-2)

Because there is a log, we need the expressions inside the log to be greater than zero:

x+2>0\text{  and  }x-2>0

We isolate the x in both inequalities and get:

x>-2\text{  and  }x>2

Intersect both results (“and”) and get the final answer:

x>2

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