Restricting the Domain

Bonjour Class! It's Melanie :)

Glad you found your way to this awesome page. Let's get started.

Something new that we learned today in class is called Restricting the Domain.

Sometimes, we are given a function which does not have an inverse. 

Thankfully we can generate an inverse that is a function over a specific interval, by effectively restricting the domain. In laymen's terms, this just means that you control or restrict the domain; all the values that are plugged into the function.

For example: Let's say your function is f(x) = x² 

If we square a negative number, our inverse will not match the original function, therefore if we restrict the domain, we can create an inverse for the original function. 

A Few Helpful Reminders:

• Remember the inverse of a relation can be created by switching the x values and the y values of the graph.
• The inverse of a relation is reflected in the line y = x
• In the inverse of a relation, the domain of the original function becomes the range, and the range of the original function becomes the domain.
• One may verify graphically or algebraically whether two functions are inverses of one another.

Here's a funny comic I found entitled "The Awkward Function"

and to finish off this post, a hue of inspiration. As Albert Einstein once said:

"Pure mathematics is, in its way, the poetry of logical ideas."

Hope y'all enjoyed this post! Gotta love pre-cal. ♥

Yours Truly,

Melanie ♥

Sources: 

http://www.mathsisfun.com/sets/function-inverse.html

http://spikedmath.com/488.html

http://www.brainyquote.com/quotes/keywords/mathematics.html