Question

For each of the following functions, state whether or not the function is one-to-one, onto, both, or neither:

1) f : Z → Z defined by f(x)=2x + 1;

2) f : R → R defined by f(x)=2x + 1;

Answer 1

1). It's a one-to-one function

2). Both one-to-one and onto function (because f(x) is increasing fun value rises from negative infinity to infinity. all real number are obtained by f(x). and particular value can be obtained by f(x) once so one-one and onto.

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