please help me with number example to understand better what is a co-vector and what is a dual vector space,as i know it is related to fact,that it eats vector,which means that it takes vector and calculates scalar,also as i know there should be used linear function,or functions which satisfies following relations

1.$f(v_1+v_2)=f(v_1)+f(v_2)$

2,$f(a*v)=a*f(v)$

so let take some vector ,let say

$V=v_1,v_2,v_3,v_4...v_n$ ok let take numbers $V=(3,4,5,6,7,8)$ and i want to calculate it's corresponding co vector,how could i solve this problem,let take this function

$f(x)=5*x$

because it is linear

$f(x_1+x_2)=f(x_1)+f(x_2)$

2.$f(a*x)=a*f(x)$

how to apply it to vector and produce co vector?please help me