TUTORIALS:

Graphing an Inverse Function
If a function f has an inverse f^{ 1}, you can use the graph of f to find the
graph of f^{ }1.
Procedure â€” To Graph the Inverse of a Function
Step 1 Identify several points (a, b) on the graph of the given
function.
Step 2 Switch the x and ycoordinates of each point to form the
points (b, a) for the inverse function.
Step 3 Plot the new points and connect them with a smooth line.
Note:
Remember, if f contains the ordered pair
(a, b), then f^{ 1} contains the ordered pair
(b, a).
Example 1
The graph of f(x) = 2x  5 is shown. Graph f^{ 1}.
Solution
Step 1 Identify several points (a, b) on the
graph of the given function.
From the graph, we choose (0, 5), (1, 3), and (4, 3).
Step 2 Switch the x and ycoordinates of
each point to form the points (b, a)
for the inverse function.
The new ordered pairs are (5, 0), (3, 1), and (3, 4).
Step 3 Plot the new points and connect
them with a smooth line
There is a visual relationship between the graphs of a function and its
inverse function. To see this, letâ€™s start with the graphs of f and f^{ 1
}from
the last example. Look at what happens when we add the graph of y = x.
Notice that the graphs of f and f^{ 1} are symmetric about the line y = x.
That is, f^{ }1 is the reflection of f about the line y = x. Similarly, f is the
reflection of f^{ 1} about the line y = x.
Note:
If the point (a, b) is on the graph
of f, then its mirror image (b, a) is
on the graph of f^{ 1}.
So, one way to get the graph of f^{ 1} is to
start with the graph of f, and reflect it
about the line y = x.
Example 2
The graph of f(x) is shown. Graph f^{ 1}.
Solution
Step 1 Identify several points (a, b) on the
graph of the given function.
From the graph, we choose (2, 6), (1, 1), (0, 2), (1, 3), and (1.4, 5).
Step 2 Switch the x and ycoordinates of
each point to form the points (b, a)
for the inverse function.The new ordered pairs are (6, 2), (1, 1), (2, 0), (3, 1) and
(5, 1.4).
Step 3 Plot the new points and connect
them with a smooth line.
Notice that f and f^{ 1} are symmetric about the line y = x.
