Q: Find the domain of h(x):
h(x) = 27 / (3-x)
A: The domain represents all of the possible x values. The best way to find the domain is to first think of what numbers x cannot be.
There are a few areas of concern when we think about domains… We need to check
So, looking at the function: h(x) = 27 / (3-x)
We know that the denominator cannot equal zero in any expression. So,
(3-x) ≠ 0
-x ≠ – 3
x ≠ 3
Therefore, x can be anything except -3.
If written in interval notation, this is: (-∞, -3) U (-3, ∞).