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Classification of Mappings

• Injective (one-one, 1-1)

  f(x)=f(y) => x=y (for all x,y in R)

• Surjective (onto)

  for every y in S there is some x in R such that f(x) in y

• Identity function

  f: R => R
  f(x)=x (for all x in R)

• Inverse function

  f:R => S injective and surjective
  g:S => R, g(y) = x <=> f(x) = y
  g=f^-1