One-one and onto functions
Sets, relations and functions · Mathematics
Study notes
Q: Classify f: R → R: (a) f(x) = 2x + 3 (b) f(x) = x^2. (a) One-one: 2a+3 = 2b+3 ⟹ a = b. Yes. Onto: for any y, x = (y-3)/2 works. Yes. Bijective. (b) Not one-one: f(2) = f(-2). Not onto: negatives never hit. Neither.