how do you prove that if {f(v1), f(v2),...f(vn) } is linearly independent where f:V to W then f is injective?

by def of LI, a linear combination of f(v1), f(v2),...f(vn) = 0 iff the coefficients are 0. so can i say that for all w in W, there is a unique linear combi of {f(v1), f(v2),...f(vn) } which will give w.

this means that w in W is unique...

and then how do i continue?