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
has a domain which is it has range:
The inverse function is:
more precisely I tacked a domain of "by hand" and it has a range
For functions means "inverse function" NOT