# invertible function by graphs

• Feb 4th 2007, 08:47 PM
gracy
invertible function by graphs
Below are the graphs of four functions. Which function is invertible?
• Feb 4th 2007, 10:22 PM
earboth
Quote:

Originally Posted by gracy
Below are the graphs of four functions. Which function is invertible?

Hello, Gracy,

first: I count 5 graphs

second: a function is invertible if the monotonicity(?) didn't change. The only graph which has this property is e).

I've added a diagram with the graph of the inverted function and the original graph e).

EB
• Feb 5th 2007, 03:45 AM
topsquark
Specifically, a function is invertible if it is 1:1, that is there is one and only one y value for each x. You can use the "horizontal line test" to determine this: pass a horizontal line through the graph of the function. If the line cuts the graph of the function in more than one place then the function has no inverse.

Note that we CAN have a (piece-wise defined) function that is increasing on some intervals and decreasing on others that is invertible.

-Dan
• Feb 5th 2007, 06:43 AM
ThePerfectHacker
Quote:

Originally Posted by topsquark
Specifically, a function is invertible if it is 1:1,

That is not good enought. It needs to be 1 to 1 and and onto. If it is not onto then it is invertible on its image. In fact any one-to-one function is invertible on its image, specifically when the it onto the image is the full function.