the tree Posted June 30, 2006 Share Posted June 30, 2006 The function [math]f:x \to , x^2 - 10x + 29 , x \in \Re , x \ge k[/math] is one-one. Find the smallest possible positive value of [math]k[/math] and the range of [math]f[/math] in this case. My understanding of "one-one" is that there can only be one value of f(x) per value of x. So I'm thinking that maybe k=5 because that is the minumum point of the function. Although I was only just introduced to the concept of "one-one" verus "one-many" so I can't be sure. Am I on the right track? Thanks. Link to comment Share on other sites More sharing options...
matt grime Posted June 30, 2006 Share Posted June 30, 2006 You have never been using the idea of 1-many. SUch things are not functions. one to one means that f(x)=f(y) implies x=y. For these purposes it is sufficient to think of drawing a horizontal line - the function will be one-one if it intersects the graph only once. Link to comment Share on other sites More sharing options...
the tree Posted June 30, 2006 Author Share Posted June 30, 2006 Never used the idea of "one-many"? Maybe my teacher said "many-one" and I misread what was on the board. Anyways, given your horizontal line (which for all intents and purposes sounds a lot like my definition), it still seems that k=5. Am I right? Link to comment Share on other sites More sharing options...
matt grime Posted June 30, 2006 Share Posted June 30, 2006 How can it be your defintion? Think about your definition - one to one means given an input there is one output. That is jsut the definition of a function. Consider my definition, given the output there is exactly one input that gets that output. e.g. x^2 is not 1-1 on R since if x^2=1 then x could be 1 or -1. It is one to one on the range x=>k whenever k is greater than or equal to 0 (which gives you your answer after translation). Link to comment Share on other sites More sharing options...
alext87 Posted July 2, 2006 Share Posted July 2, 2006 k is 5 as this is the minimum found by equating the derivative to zero and rearranging. The range is greater than or equal to 4 as this is the value min y value. It is one-one in this case. One-many does not exist as a name! but only one-one function has inverses!?-is this what you mean!? Link to comment Share on other sites More sharing options...
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