# How to determine the new domain and range given the old domain and range?

"A function f(x) has domain $\{x \in \mathbb{R}\;|\;x \ge -4\}$ and range $\{y \in \mathbb{R}\;|\;y \lt -1\}$ Determine the domain and range of each function without graphing."

I was given the $2$ functions $y=f(-x)$ and $y=-2f(-x+5) + 1$. For the first function, I understand why the the domain is $x \lt 4$ (everything is flipped because of $-1$), but I don't understand why it doesn't say that $x \le 4$.

For the second function, I don't understand why the range doesn't say $y$ $\gt 3$ . I also don't understand why the domain isn't $x \le -1$. Hopefully this post made sense.

• Please check the first sentence in the last paragraph: "is less is greater than $1$" does not make sense. Also, please read this tutorial on how to typeset mathematics on this site. Using the proper mathematical symbolism would make your post easier to read. – N. F. Taussig Oct 2 '16 at 21:51
• I don't understand how the LaTeX works. I typed y \ge 3 but it didn't work. – Hamze Oct 2 '16 at 22:39