Definition: Image and Preimage

• Let A and B be two sets and f a function from A to B. Then the image of f is defined as
  • imag(f) = {b B : there is an a A with f(a) = b}.
• Let A and B be two sets and f a function from A to B. If C is a subset of the range B then the preimage, or inverse image, of C under the function f is the set defined as
  • f ^-1 (C) = {x A : f(x) C }