Discrete maths about one to one

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August 19th 2009, 06:51 PM
quah13579

Discrete maths about one to one

(a). Define the function f:
$<br /> \mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\<br />$
by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?
(Justify your answer)

(b). Define the function g:
$<br /> \mathbb{R}\rightarrow\mathbb{R}^{2} \\<br />$
by g(x) = (x+1, x+2). Is g onto?
(Justify your answer)

thanks!(Happy)

My answer
(a) Yes
(b) i am not sure about this one

How to justify these?
August 19th 2009, 07:09 PM
quah13579

Discrete maths

(a). Define the function f:
$<br /> \mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\<br />$
by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?
(Justify your answer)

(b). Define the function g:
$<br /> \mathbb{R}\rightarrow\mathbb{R}^{2} \\<br />$
by g(x) = (x+1, x+2). Is g onto?
(Justify your answer)

thanks!
August 19th 2009, 07:31 PM
ynj

Quote:

Originally Posted by quah13579

(a). Define the function f:
$<br /> \mathbb{R}^{2}\rightarrow\mathbb{R}^{2} \\<br />$
by f(x,y) = (x+2y, 3x+4y). Is f one-to-one?
(Justify your answer)

(b). Define the function g:
$<br /> \mathbb{R}\rightarrow\mathbb{R}^{2} \\<br />$
by g(x) = (x+1, x+2). Is g onto?
(Justify your answer)

thanks!

(a)yes
(b)no
August 19th 2009, 07:52 PM
Gamma

a) the matrix representing this equation is invertible
b) is the point (3,5) in the image of this function?
ynj is correct

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