(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?

(Justify your answer)

(b). Define the function g:

$\displaystyle

\mathbb{R}\rightarrow\mathbb{R}^{2} \\

$

by g(x) = (x+1, x+2). Is g onto?

(Justify your answer)

thanks!

My answer

(a) Yes

(b) i am not sure about this one

How to justify these?