# Thread: Find the domain of f(x) = ln(x+1)

1. ## Find the domain of f(x) = ln(x+1)

Please help, I looked in my book to find an explanation for this and found nothing that made sense.

How do I begin to find the domain for:

f(x) = ln(x+1)

Please provide steps (if possible), Thanks!

2. Originally Posted by lilrhino
Please help, I looked in my book to find an explanation for this and found nothing that made sense.

How do I begin to find the domain for:

f(x) = ln(x+1)

Please provide steps (if possible), Thanks!
Step one: What values of x can we plug into the equation and still get a solution? Included with this question is: What values of x can we not plug into the equation to get a solution?

Since the function is log, we know that we cannot take the log (ln in this case) of a negative number or of 0, so the term inside the function must be >0.

Step two: Find these values of x.

The term inside the log is (x + 1), so:
(x + 1) > 0
x > -1

That is your domain, which can be written as:
D = (-1,inf)

3. Originally Posted by ecMathGeek
Step one: What values of x can we plug into the equation and still get a solution? Included with this question is: What values of x can we not plug into the equation to get a solution?

Since the function is log, we know that we cannot take the log (ln in this case) of a negative number or of 0, so the term inside the function must be >0.

Step two: Find these values of x.

The term inside the log is (x + 1), so:
(x + 1) > 0
x > -1

That is your domain, which can be written as:
D = (-1,inf)
Since we can plug an infinite amount of numbers in - I guess that's where we get our infinity portion of the answer.

But, how do you determine how you actually write out the answer? Is it because you begin with -1 and end with an infinite amount of solutions?

I'll have to memorize the rule that we can't take the log of 0 or a negative number so that's how we get the (x + 1) > 0

Thank you so much for your response

4. Originally Posted by lilrhino
Since we can plug an infinite amount of numbers in - I guess that's where we get our infinity portion of the answer.

But, how do you determine how you actually write out the answer? Is it because you begin with -1 and end with an infinite amount of solutions?

I'll have to memorize the rule that we can't take the log of 0 or a negative number so that's how we get the (x + 1) > 0

Thank you so much for your response
When I said that the domain is x > -1, this indicates that x is all real numbers greater than -1. We can denote this by saying that x "is all values from -1 to infinity, not including infinity or -1" which we write as (-1,inf).

If, for example, the domain was x < 10, the domain would be "all values less than 10" which is "all numbers from negative infinity to 10," which can be written as (-inf,10).