What is the domain of (f(x)=\frac{x+1}{x+1})?

Correct answer: (\mathbb{R}\setminus{-1})

The direct answer is option B: ℝ\{−1}. The domain is the set of inputs for which the original expression is meaningful. In f(x)=(x+1)/(x+1), the denominator x+1 cannot equal zero. Solving x+1=0 gives x=−1, so −1 must be excluded. For every other real x, the fraction is defined and simplifies numerically to 1, although the original function still has a missing point at −1. Therefore the domain is ℝ\{−1}. Option A, ℝ, is wrong because it includes −1, where the denominator is zero. Option B is correct because it removes exactly that forbidden input. Option C, {1}, is wrong because it gives only one input; many other real inputs are allowed. Option D, (−1,∞), is wrong because values less than −1, such as −2, are also valid; only −1 is forbidden. A crucial exam warning is never to cancel the common factor before recording the original denominator restriction. The simplified expression is 1, but the original function is not defined at −1.