SOLUTION: How to take the domain of: sqrt(x-1)-ln(15-x) Please show how to solve Thank you

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Question 1006911: How to take the domain of:
sqrt(x-1)-ln(15-x)
Please show how to solve
Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
No log of negative number, so ln(15-x) can only accept .

The square root must be for non-negative argument, so x-1 must be nonnegative.

The domain is the intersection of these requirements.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

How to take the domain of:
sqrt(x-1)-ln(15-x)
Please show how to solve
Thank you

Set each expression > 0, since the domain MUST be POSITIVE
We then get: x - 1 > 0______x > 1
Also, 15 - x > 0
- x > - 15
---- Inequality sign changes when dividing by a negative number (< 0)
x < 15
Therefore, domain, or