use the given function f to answer parts (a) ...
use the given function f to answer parts (a) through (f). f(x)= -6 + ln x a. the vertical asymptote of f is x = 0. (simplify your answe b. there is no vertical asymptote. (d) find f⁻¹, the inverse of f. f⁻¹(x)=e^(x + 6) (simplify your answer.) (e) find the domain and range of f⁻¹. the domain of f⁻¹ is. (type your answer in interval notation.)
Answer
# Explanation:
## Step1: Recall domain - range relationship of inverse functions
The domain of the inverse function $f^{-1}(x)$ is the range of the original function $f(x)$, and the range of $f^{-1}(x)$ is the domain of $f(x)$.
## Step2: Determine the range of the original function $f(x)=-6 + \ln x$
The natural - logarithm function $y = \ln x$ has a range of $(-\infty,\infty)$. So, for $y=-6+\ln x$, the range is also $(-\infty,\infty)$.
# Answer:
$(-\infty,\infty)$