November 14th, 2017, 04:04 PM  #1 
Newbie Joined: Nov 2017 From: Maryland Posts: 1 Thanks: 0  Deriving Functions Problem
Suppose that g is a real valued, differentiable function whose derivative g' satisfies the inequality g'(x)less than or equal to M for all x in R. Show that if epsilon is greater than 0 is small enough, then the real valued function f defined by f(x)=x+epsilon*g(x) is one to one and onto. Recall that a function f is said to be "one to one" if x sub 1 does not equal x sub 2 implies that f(x sub 1) does not equal f(x sub 2), and f is said to be "onto" if for every real number y, there is a real number x such that f(x) = y. 
November 14th, 2017, 04:07 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,825 Thanks: 1051 Math Focus: Elementary mathematics and beyond 
Have you made any progress on this?


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