Math 111 - Oct 28, 2011

5.1 Inverse functions...

A relation is any set of ordered pairs or equation with x&y...

An inverse of a relation switches the x&y. See red above.

Remember that a function is a relation that doesn't have repeated x values.

You can tell it's a function if it passes the vertical line test.

It's inverse will be a function if the original passes the horizontal line test.

A function that also passes the horizontal line test - (so its inverse will be a function) is called "one-to-one".

If a function is one-to-one its inverse is also a one-to-one function and we can usually "find" it algebraically....

has a domain of has a range

It's inverse is: since this is one-to-one: we can solve it for y.

has a range of has a domain

Because we just swapped x and y...

The domain of the original is the range of the inverse

The range of the original is the domain of the inverse

Another:

has a domain which is it has range:

The inverse function is:

sorta

more precisely I tacked a domain of "by hand" and it has a range

For functions means "inverse function" NOT