# What is the range of the function f(x)=3 - ln(x+2) #?

$y \setminus \in \mathbb{R}$
The range of $f \left(x\right) = \ln \left(x\right)$ is $y \setminus \in \mathbb{R}$.
The transformations done to get $3 - \ln \left(x + 2\right)$ are to shift the graph 2 units left, 3 units up, and then reflect it over the $x$-axis. Of those, both the shift up and the reflection could change the range, but not if the range is already all real numbers, so the range is still $y \setminus \in \mathbb{R}$.