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 (type your answer in interval notation.) determine the vertical asymptote of f, if it exists. select the correct choice and, if necessary, complete your choice. a. the vertical asymptote of f is x = 0. (simplify your answer.) b. there is no vertical asymptote. (d) find f⁻¹, the inverse of f. f⁻¹(x)= (simplify your answer.)
Answer
# Explanation:
## Step1: Set \(y = f(x)\)
Let \(y=-6 + \ln x\).
## Step2: Solve for \(x\) in terms of \(y\)
First, add 6 to both sides: \(y + 6=\ln x\). Then, use the property that if \(y=\ln x\), then \(x = e^{y}\). So \(x=e^{y + 6}\).
## Step3: Replace \(x\) with \(f^{-1}(x)\) and \(y\) with \(x\)
We get \(f^{-1}(x)=e^{x + 6}\).
# Answer:
\(e^{x + 6}\)