one to one function?

Question

Are these one-to-one functions?

1. f(x)=1/x
2. f(x)=7x-3
3. f(x)=x^4-5
4. f(x)= absolute value of x-1

How do you know?

Answer 1

A one-to-one function is a function f such that if f(x)=f(y), then x=y. Another way to say that is that if x=/=y (not equal), then f(x)=/=f(y). That is, the function maps distinct objects to distinct objects.

Because of these properties, the horizontal line test can be used to check for one-to-one-ness in the plane.

Answer 2

Ouch. Some very interesting answers so far.

Here's what you're looking for. :-)

One to one function means that for every value you put into the function, it corresponds to only one number in the results side. X^2 for example is not a one to one function since 1^2 and -1^2 both map to 1.

One to many allows you to put one value in and get several answers out.

So for your exercise, just start putting numbers in.

I like to start with 0, then 1, then -1, then 2, etc, and see what I get. Just do the same and you'll have your answers!

Answer 3

if you substitute x with 1.. the result will be one

f(x)=1/x
f(1)=(1/1)
f(1)=1 (YES)

fi(x)=7x-3
f(1)=7(1)-3
f(1)=7-3
f(1)=4 (NO)

do the rest

i think.. not sure though.