1. The problem statement, all variables and given/known data Determine whether each of the following mappings f is onto or one-to-one. Is f an isomorphism? 1) f maps R2 to R3 defined by f(x, y) = (x, y, x+y) 2) f maps R3 to R(1x3) defined by f(x,y,z) = [x^2, y^2, z^2] 3) f maps R4 to P2(R) defined by f(a,b,c,d) = a+(b-c)x+dx^2 2. Relevant equations 3. The attempt at a solution I'm not sure how to do these.. I understand somewhat about one-to-one and onto, but these notations kind of confuse me.. For onto, do I just need to look at the outcome and see if it spans the space? And for one-to-one, I look at rather every component from the source appears in every component in the result? 1) Not one-to-one, onto. 2) Not one to one, onto. 3) Not one to one, onto.