function

chipatel87

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Nov 20, 2011
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define Z-----> such f(n)= 2-5n for all integers n

is f one to one? prove or give counterexample
if f onto? prove or give a counterexample
 
define Z-----> such f(n)= 2-5n for all integers n

is f one to one? prove or give counterexample
if f onto? prove or give a counterexample
Every linear function \(\displaystyle f:\mathbb{R}\to\mathbb{R}:~x\mapsto mx+b\) is both one-to-one and onto.

However in this case the function \(\displaystyle f:\mathbb{Z}\to\mathbb{Z}\).
Can it be onto?
 
this is what i have

in order to prove it is one to one
suppose 2-5(n1)=2-5(N2)
-2 -2
-5(n1)=-5(n2)
/-5 /-5
n1 = n2
this makes it one to one

for onto i am showind 1=2-5n
-1/5=n
because it does not equal to 1 it is not onto?

is my proof correct?
 
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