Abstract Algebra: Theory and Applications · Problem 1.19

Preliminaries — Thomas Judson

Mathematics — Abstract Algebra · functions-bijections-cardinality

Problem

Determine whether each of the following functions is one-to-one and whether it is onto. ((a))

f : \mathbb{Z} \to \mathbb{Z}

defined by

f(n) = n^2

; ((b))

f : \mathbb{Z} \to \mathbb{Z}

defined by

f(n) = n + 3

; ((c))

f : \mathbb{R} \to \mathbb{R}

defined by

f(x) = x^2

; ((d))

f : \mathbb{R} \to \mathbb{R}

defined by

f(x) = e^x

; ((e))

f : \mathbb{R} \to \mathbb{R}

defined by

f(x) = x^3 - x