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.

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.

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?

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).

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!?