Find the domain of g ( x ) = ln &#x2061;<!-- ⁡ --> ( <mrow class

tilfaen4a

tilfaen4a

Answered question

2022-05-21

Find the domain of g ( x ) = ln ( x x 1 )
I know the argument of the function has to be greater than 0, so:
( x x 1 ) > 0 x > 0
however in this case x 1, x 0 as they result in an answer which is undefined, so I think it's reasonable for me to say the domain is x > 1, however this is not the correct answer.

Answer & Explanation

ol5ick189

ol5ick189

Beginner2022-05-22Added 7 answers

To find the actual intervals on which the function is defined, what we need is:
( x 1 > 0  AND  x > 0 x > 1 )  or else  ( x 1 < 0 AND x < 0 x < 0 )
So the the function's domain is given by
( , 0 ) ( 1 , )
Shamar Reese

Shamar Reese

Beginner2022-05-23Added 1 answers

Hint: In order for x x 1 to be positive, the numerator and denominator must have the same sign.

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