Question

Determine if f: R x R --> R x R f(x,y) = (2x, 3y) is onto.
How do I go about figuring this out?

Answer 1

A function is onto if range =co-domain

Answer 2

I know that, but I'm confused about the notation I guess. What is the significance of ℝxℝ

Answer 3

It means it is a function with domain and co domain as R(Set of real numbers)

Answer 4

Why not just say ℝ → ℝ then?

Answer 5

it represents cross product

Answer 6

ie we get the relation in ordered pairs

Answer 7

*cartesian product is better term

Answer 8

http://en.wikipedia.org/wiki/Cartesian_product

Answer 9

I know that it's an ordered pair but what I'm confused about is how to apply that to the function to see if it's onto or not. I'm also confused as to why the function is shown as an ordered pair as well.

Answer 10

in cartesian product we represent function in ordered pairs (x,y) where first element is the x value that we put in function (independent variable) ,and y is the output(dependent value).

Answer 11

if RxR is an ordered pair and it goes to another ordered pair how do I put that in the function though

Answer 12

RXR is a set of ordered pairs relating two sets

Answer 13

note all functions are relations :)

Answer 14

R^2 -> R^2: f(x,y) = (2x, 3y)

set it up as:

2x + 0y = x
0x + 3y = y

sounds familiar

Answer 15

\[Ax=b\]
\[\begin{pmatrix}2&0\\0&3\end{pmatrix}\binom{x}{y}=\binom{x_1}{y_1}\]

Answer 16

is the range of this equal to its codomain?

Answer 17

Definition: A mapping T: R^n -> R^m is said to be ONTO R^m if each "b" in R^m is the image of (can be obtained by) "at least one x" in R^n.

http://www.smccd.edu/accounts/leache/062m270a/documents/m270h07lineartransformations.pdf

Answer 18

since A is linearly independant, id say that fits well

Answer 19

wow, thank you so much

Answer 20

youre welcome