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Domain of One Variable Function – A function with sum of ln’s – Exercise 2443

Exercise

Determine the domain of the function:

f(x)=\ln (x+2)+\ln (x-3)

Final Answer


x>3

Solution

Let’s find the domain of the function:

f(x)=\ln (x+2)+\ln (x-3)

Because there are ln’s, we need the expressions inside the ln’s to be greater than zero:

x+2>0\text{  and  }x-3>0

We got two inequalities. We’ll arrange them:

x+2>0 \Longrightarrow x>-2

x-3>0 \Longrightarrow x>3

Intersect both inequalities:

x>-2 \text{  and  } x>3 \Longrightarrow x>3

Hence, the domain of the function is

x>3

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