Inverse of a Function and Restricted Domain

Hello Class! Navjot here!

Today we learned Restricted Domain and Inverse of a Function!  What does this mean? Well.... sometimes we have a function whose inverse is not a function. In this case you would restrict the domain of f(x) so that f^-1(x) is also a function.  

Example:

• Find the inverse of y = x² + 1

From the graph you can clearly tell that the inverse of this function would not be a function, since it would not pass the vertical line test. In order to make this a function we would have to restrict the domain.

 In this graph the domain has been restricted to include only numbers that are less than 0. By doing this, the inverse of this function becomes a function. 

The domain for the original function is x < 0 and the range would be 1 < y, therefore the domain for the inverse function would be 1 < x and the range would be y < 0.

 

REMEMBER: The domain of the original function becomes the range for the inverse and the range of the original function becomes the domain of the inverse!

I hope that this make sense and that you all learned something! And now I'll leave you with a joke:

Why do they never serve beer at a math party?

Because you can't drink and derive... 

 

 

Also,

 

Sources: http://www.purplemath.com/modules/invrsfcn3.htm#previous