9514 1404 393
Answer:
B. (-∞, 1) ∪ (1, 2]
Step-by-step explanation:
When you are looking for answers to domain questions, you are looking for values of the variable(s) that make the function undefined. Here, there is a square root involved, and the rational function has a denominator that might be zero.
The function is only defined for square roots of non-negative numbers. That is ...
2-x ≥ 0 ⇒ x ≤ 2
The rational function is only defined for non-zero denominators, so ...
x-1 ≠ 0
x ≠ 1
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So, you're looking for a domain description that includes all numbers less than or equal to 2, and excludes x=1. The attached number line shows a graph of this.
The domain divides into two parts: all numbers less than 1, and those numbers between 1 and 2 (including 2). This will be the union ...
(-∞, 1) ∪ (1, 2]
