# Discrete maths about one to one

• Aug 19th 2009, 06:51 PM
quah13579
Discrete maths about one to one
(a). Define the function f:
$\displaystyle \mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\$
by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?

(b). Define the function g:
$\displaystyle \mathbb{R}\rightarrow\mathbb{R}^{2} \\$
by g(x) = (x+1, x+2). Is g onto?

thanks!(Happy)

(a) Yes

How to justify these?
• Aug 19th 2009, 07:09 PM
quah13579
Discrete maths
(a). Define the function f:
$\displaystyle \mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\$
by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?

(b). Define the function g:
$\displaystyle \mathbb{R}\rightarrow\mathbb{R}^{2} \\$
by g(x) = (x+1, x+2). Is g onto?

thanks!
• Aug 19th 2009, 07:31 PM
ynj
Quote:

Originally Posted by quah13579
(a). Define the function f:
$\displaystyle \mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\$
by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?

(b). Define the function g:
$\displaystyle \mathbb{R}\rightarrow\mathbb{R}^{2} \\$
by g(x) = (x+1, x+2). Is g onto?