How do I express a Domain that is from -(1/4) to infinite except 0?
I saw that last year and I forgot lol
Thanx in advance!
There are a few different ways. You could, for example, say that the domain is $\displaystyle \left\{x\in\mathbb{R}\;\bigg|\;x > -\frac14,\;x\neq0\right\}$, or you could state it more concisely as $\displaystyle \left(-\frac14,\;\infty\right) - \{0\}$ (here the "$\displaystyle -$" denotes the difference of the sets). A simpler way is to just state that the domain is the set of nonzero real numbers that are greater than $\displaystyle \frac14$.
Or possibly: In interval notation
$\displaystyle \left(-\frac{1}{4},0\right) \ \ \bigcup \ \ \bigg(0, +\infty\bigg)$
But, do we know if $\displaystyle -\frac{1}{4}$ is included in the interval?
If it is, then the notation would change to:
$\displaystyle \left[-\frac{1}{4},0\right) \ \ \bigcup \ \ \bigg(0, +\infty\bigg)$