QuestionSuppose that $f(x)=1+3^{x}$. (a) Sketch a graph of $f$. Then sketch the graph of $f^{-1}(x)$ on the same coordinate axes. Remember, inverse functions switch their $x$ and $y$ values. To do this, it may be easiest to make a table of values for $f$, and then reverse those values (switching $x$ and $y$ columns) for $f^{-1}$.

Studdy Solution
Using the table of values for $f^{-1}(x)$, plot the points $(1.11, -2), (1.33, -1), (2, 0), (4, 1), (10, 2)$ on the same coordinate plane.
Draw a smooth curve through these points to represent the graph of $f^{-1}(x)$.
The graph of $f(x) = 1 + 3^x$ and its inverse $f^{-1}(x)$ are now sketched on the same coordinate axes.