Your textbook's coverage
of inverse functions probably came in two parts. The first part had lots
of curly-braces and lists of points; the second part has lots of "y="
or "f(x)="
functions that you have to find the inverses for, if possible. The first
part will show up in your homework and maybe on a test; the second part
will definitely show up on your test, and you might even use it in later
classes.

The inverse of a function
has all the same points as the original function, except that the x's
and y's
have been reversed. This is what they were trying to explain with their
sets of points. For instance, supposing your function is made up of these
points: {
(1, 0), (–3, 5), (0, 4) }.
Then the inverse is given by this set of point: {
(0, 1), (5, –3), (4, 0) }.
(Note that the order of the points doesn't matter; you can rearrange the
points so the x's
are "in order", or not. It's your choice.)

Once you've found the inverse
of a function, the question then becomes: "Is this inverse also a
function?" Using the set of points from above, the function above
graphs like this:

You know that this is a
function (and you can check quickly by using the Vertical
Line Test): you
don't have two different points that share the same x-value.
The inverse graph is the blue dots below:

Since the blue dots (the
points of the inverse) don't have any two points sharing an x-value,
this inverse is also a function.

Finding
the inverse from a graph

Your textbook probably
went on at length about how the inverse is "a reflection in the line
y = x".
What it was trying to say was that you could take your function, draw
the line y
= x (which is the
bottom-left to top-right diagonal), put a two-sided mirror on this line,
and you could "see" the inverse reflected in the mirror. Practically
speaking, this "reflection" property can help you draw the inverse:

Stapel, Elizabeth.
"Inverse Functions: Definition of 'Inverse' / Drawing the Inverse
From a Graph." Purplemath.
Available from https://www.purplemath.com/modules/invrsfcn.htm.
Accessed