Find the domain of the function. $$ f(x)=\log \left(\frac{3}{x+2}\right) $$ Write your answer as an interval or union of intervals. Domain:

Question

UpStudy AI · Accepted Answer

We need the expression inside the logarithm to be positive because the logarithm is only defined for positive arguments.

1. The argument of the logarithm is $$\frac{3}{x+2}$$. We set up the inequality:
   $$
   \frac{3}{x+2} > 0
   $$

2. Since $$3$$ is positive, the entire fraction is positive when the denominator is also positive. So we require:
   $$
   x + 2 > 0
   $$

3. Solve for $$x$$:
   $$
   x > -2
   $$

Thus, the domain of $$f(x)$$ is:
$$
(-2,\, \infty)
$$
The domain of $$ f(x) = \log\left(\frac{3}{x+2}\right) $$ is $$ (-2, \infty) $$.

Find the domain of the function.

Write your answer as an interval or union of intervals.
Domain: