One-to-one functions

[1141]

Can anybody help?

I've been doing functions recently, and been breezing through it, until I came to one-to-one or one-on-one functions. I understand what they are, but my text book expects me to be able to determine whether a function is one-to-one WITHOUT even giving me a method to use or even an example to work from.

So can anybody please tell me how to determine whether a function is one-to-one or not?

The questions I have are:

Each of the following functions has domain ?. Determine which are one-to-one functions.

a.) f : x ? 3x + 4
b.) f : x ? x[sup:59ryifo7]2[/sup:59ryifo7] + 1

 

[toidayma]

You can use this article to solve your problem http://www.analyzemath.com/OneToOneFunct/OneToOneFunct.html
a) f(x) = 3x + 4 is a one - to - one function because:
---> let x1, x2 are elements of R, and x1 is not equal to x2, we have f(x1) is not equal to f(x2).
Or contrapositive: let x1, x2 are elements of R so that f(x1) = f(x2), we have to prove that x1 = x2 then. Easy for this one.
b) f(x) = x^2 + 1 is not a one - to one function.
We shall prove this by using the property of one-to-one function.
ie: we will prove that with x1 an element of R, there is another x2 that x2 <> x1 but f(x1) = f(x2)
In this case, let x2 = -x1. We then have, f(x1) = x1^2 +1
and f(x2) = (-x1)^2 +1 = (x1)^2 +1 = f(x1)
Thus, this function is not a one-to-one function.