1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Injective function

  1. May 14, 2005 #1
    is a cubic function injective for all real numbers?
     
  2. jcsd
  3. May 14, 2005 #2

    Pyrrhus

    User Avatar
    Homework Helper

    Yes it's an injective function.
     
  4. May 14, 2005 #3

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    depends on your definition of a "cubic function".

    the function f(x) = x^3 + bx^2 + cx + d, could be considred a cubic function.

    it is injective if and only if the derivative f'(x) = 3x^2 + 2bx + c never changes sign.

    e.g. f(x) = x^3 is injective because f'(x) = 3x^2 is never negative.

    but f(x) = x^3 - x is not injective becuase f'(x) = 3x^2 - 1 is positive for x = 1 and negative for x = 0.
     
  5. May 14, 2005 #4

    Pyrrhus

    User Avatar
    Homework Helper

    Also because to have an inverse function [itex] f^{-1} (x) [/itex] it must be bijective (injective and surjective).
     
  6. May 18, 2005 #5
    Well Thx A Great Deal Guys I'm Struggling With First Year Maths And This Site Really Helps, Thx A Million
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Injective function
Loading...