Question

(c) from the graph, determine the range and any asymptotes of f.
the range of f is (-\infty,\infty).
(type your answer in interval notation.)
determine the vertical asymptote of f, if it exists. select the correct choice and, if necessary, fill in the answer box to complete
a. the vertical asymptote of f is x = -3.
(simplify your answer.)
b. there is no vertical asymptote.
(d) find f^{-1}, the inverse of f.
f^{-1}(x)=e^{x}-3 (simplify your answer.)
(e) find the domain and range of f^{-1}.
the domain of f^{-1} is (-\infty,\infty).
(type your answer in interval notation.)
the range of f^{-1} is
(type your answer in interval notation.)

Explanation:

Step1: Recall the property of inverse function

The domain of \(y = f(x)\) is the range of \(y = f^{-1}(x)\), and the range of \(y = f(x)\) is the domain of \(y = f^{-1}(x)\).

Step2: Use the given information

We know that the range of \(f(x)\) is \((-\infty,\infty)\) (from part (c)).

Answer:

\((-\infty,\infty)\)