SOLUTION: Find the domain of the function f(x) = ln ((x+3)/(x-2))

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Question 1199978: Find the domain of the function f(x) = ln ((x+3)/(x-2))
Answer by ikleyn(52903) About Me  (Show Source):
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Find the domain of the function f(x) = ln ((x+3)/(x-2))
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The argument under the logarithm must be positive

    %28x%2B3%29%2F%28x-2%29 > 0.


So, there are two cases: 

    (a)  either x+3 > 0  and  x-2 > 0

    (b)  or     x+3 < 0  and  x-2 < 0.


In case (a),  x > -3  and  x > 2,  which implies  x > 2.

In case (b),  x < -3  and  x < 2, which implies  x < -3.


ANSWER.  The domain of the function  ln%28%28x%2B3%29%2F%28x-2%29%29  is the union of two sets (-oo,-3) U (2,oo).

Solved.