Proving f(x) = x + cos x has an inverse without graphing

[mmlm01]

I need to show that the function {f(x)= x + cos x} has an inverse without the use of a graph. The professor has asked us to think intuitively about this problem, and I am just at a loss. Any help would be most appreciated, as I am trying not to fail this class. Thanks!

 

[hypermorphism]

I need to show that the function {f(x)= x + cos x} has an inverse without the use of a graph. The professor has asked us to think intuitively about this problem, and I am just at a loss. Any help would be most appreciated, as I am trying not to fail this class. Thanks!

You can tell how a function behaves without drawing a graph. Think about this: y=x has an inverse and y=x³ has an inverse, but y=x² and y=cos(x) don't have global inverses. Have you learned about derivatives ? What is true about the first two functions that isn't true about the second two functions ?
How could you get the graph of an inverse given the graph of a function ? What does the "vertical line test" mean ? What kind of test would you use for inverses ? How does this test connect with derivatives ?

 

[Hurkyl]

https://www.physicsforums.com/showthread.php?t=70584

Don't multiple post.