### MCR3U Unit 1 Lesson 11 Lesson Plan

#### Domain and Range

Watch the video below on finding the domain and range of inverse functions,

### Domain and Range of Inverse Functions | Mathematics

### Restricting the Domain and Range Review

As it stands the function above does not have an inverse, because some y-values will have more than one x-value. But we could restrict the domain so there is a unique x for every y

Now we can have an inverse:

Let’s plot them both in terms of x … so it is now f-1(x), not f-1(y):

#### Restricting Domain and Range for Quadratic Function

#### Example 2

Find the inverse function of f(x) = x2 + 2, x ≥0, if it exists. State its domain and range.

This same quadratic function, as seen in Example 1, has a restriction on its domain which is x ≥0. After plotting the function in xy−axis, I can see that the graph is a parabola cut in half for all x values equal to or greater than zero. This should pass the Horizontal Line Test which tells me that I can actually find its inverse function by following the suggested steps.

In its graph below, I clearly defined the domain and range because I will need this information to help me identify the correct inverse function in the end.

Remember that the domain and range of the inverse function come from the range, and domain of the original function, respectively. It’s called the swapping of domain and range.

Even without solving for the inverse function just yet, I can easily identify its domain and range using the information from the graph of the original function: domain is x ≥ 2 and range is y ≥ 0.

Now, let’s go ahead and algebraically solve for its inverse.

Graphing the original function with its inverse in the same coordinate axis.