Find the domain of f(x) = ln(7 - x^2)/2 So I solve for this inequality, because the argument of the natural log must be strictly greater than 0. 7 - x^2 0 7 x^2 \sqrt{7} \sqrt{x^2} \sqrt{7} |x| Which in interval notation, is: ( -\sqrt{7}, \sqrt{7} ) But this is "wrong" for some reason. Would someone point out why please?

Question

Find the domain of f(x) = ln(7 - x^2)/2
So I solve for this inequality, because the argument of the natural log must be strictly greater than 0.

7 - x^2 > 0
7 > x^2
\sqrt{7} > \sqrt{x^2}
<=> 
\sqrt{7} > |x|

Which in interval notation, is:
( -\sqrt{7}, \sqrt{7} )

But this is "wrong" for some reason. Would someone point out why please?

jamesj · Answer

If you want the domain of
$$f(x) = \frac{ \ln(7 - x^2)}{2}$$
or even
$$f(x) = \ln \left( \frac{7-x^2}{2} \right)$$
then what you've done is exactly right.

Note in both cases x CAN have negative values.  For example, if x = -1, then 7 - x^2 = 6, and we can evaluate either function.

anonymous · Answer

So this domain on this interval: ( -\sqrt{7}, \sqrt{7} ) , is correct?

jamesj · Answer

For the problem you've given us, yes.  Why do you think it's wrong?

anonymous · Answer

I entered this on my electronc web assignment and it says that is wrong

jamesj · Answer

pesky web assignments.