Let f, g and h be the following functions.
$f:Z \rightarrow \{-1,1\} \text{ defined as } f(x) =\begin{cases} 1, & \text{if $ x $ is even} \\ -1, & \text{if $ x $ is odd} \end{cases} $
$ g:Z \rightarrow R \text{ defined as } g(x) = x^2 - \frac 12 $
$ h:\{x|x\in R \land x \ge 0 \} \rightarrow R \text{ defined as } h(x) =\sqrt{\mathstrut x} + 2 $
Determine the range of $ f,g $ and $ h $
My answers are $\{1,1\}$ for $f$
The range of $f$ is $$\{-1,1\}$$
The range of $g$ is $$\{-1/2, 1/2, 7/2, 17/2, 31/2, ..., (2n^2-1)/2,...\}$$
The range of $h$ is the interval $$[2, \infty)$$