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Abstract Algebra-Functions One-to-One

Which of the following functions is one-to-one? onto?
1. f: R^+---->R^+ given by f(x)=x^2 - x +1
2. g: R^2----->R^2 given by 2x2 matrix 2 -1(as the first row) and 4 -2(as the second row)

Solution Preview

Both functions are neither ono-to-one nor onto for the following reasons.


one-to-one functions have the property that if f(a) = f(b) then a must equal b

onto functions have the property that for every y in the codomain there is an x in the domain ...