Answer
Option (c)
Work Step by Step
RECALL:
The domain of the logarithmic function $f(x) = \log_a{x}, a\gt 0, a\ne 1$ is $x \gt0$.
Thus, to find the domain of $f(x) = \log_3{(x+2)}$, the value of $x+2$ must be greater than 0.
So
$x+2 \gt 0
\\x \gt 0-2
\\x \gt -2$
Therefore, the answer is Option (c).