Consider the function $f(x)=e^x$.

1. What is its inverse function, $f^{−1}(x)?$

   Step 1(a):

   If the function is $y = e^x$ the the inverse function is $x = e^y$. Now solve for $y$.

2. Investigate $f(x)$ and $f^{-1}(x)$.

   Hint (b):

   Graph each function. State each function's domain, range, asymptote(s), and intercept(s).

3. For what integer value of $n$ is the graph of $f^{−1}(x)$ between the graphs of $y = log_n$ $x$ and $y = log_{n+1^x}?$

   Hint (c):

   ln $x = log_ex$
   What is the value of $e?$

4. For what values of $x$ is the graph of $f^{−1}(x)$ above each of the graphs in your answer to part (c)? For what $x$-values is it below?

   Hint (d):

   When does ln$(x)=log_2(x) = log_3(x)?$