This question is from the book Abstract Algebra: Theory and Applications by Thomas W. Judson.
Chapter 1 – Question 18
Determine which of the following functions are one-to-one and which are onto. If the function is not onto, determine its range.
(a) $f : \mathbb{R} \to \mathbb{R}$ defined by $f(x) = e^x$
(b) $f : \mathbb{Z} \to \mathbb{Z}$ defined by $f(n) = n^2 + 3$
(c) $f : \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \sin x$
(d) $f : \mathbb{Z} \to \mathbb{Z}$ defined by $f(x) = x^2$