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Need help to show f(x)=x + cos x has an inverse w/out graph

  1. Apr 8, 2005 #1
    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!
  2. jcsd
  3. Apr 8, 2005 #2
    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 ?
  4. Apr 8, 2005 #3


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