Final answer:
The domain of the function f(x) = 1/(x+1) is all real numbers except -1, because -1 would make the denominator zero and the function undefined. This can be expressed as D = (-∞, -1) U (-1, ∞) in mathematical notation.
Step-by-step explanation:
In mathematics, the domain of a function is the set of input values that the function can handle correctly. In your function f(x) = 1/(x+1), the denominator cannot be equal to 0, so the value of x cannot be -1. Because if x equals -1, then the denominator becomes zero, causing undefined behavior. Therefore, the domain of the function is all real numbers except -1.
To express the domain using mathematical notation, you can write the domain as D = (-∞, -1) U (-1, ∞), where U represents the union of the two intervals, and -∞ and ∞ represent negative infinity and positive infinity respectively.
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