What is the domain of f(x) = (x² + 1)/(x² - 1)?

Correct answer: R \ {-1, 1}

For a rational function, the denominator must be non-zero. Set x² - 1 = 0 and factor it as (x - 1)(x + 1) = 0. This gives x = 1 or x = -1, so those two inputs are excluded. The numerator x² + 1 is defined for every real x and therefore creates no additional restriction. All other real numbers make the denominator non-zero and give a valid real output. Consequently the domain is R \ {-1, 1}, which is option A. Option B excludes 0 even though the function is defined there, option C keeps only the interval between the forbidden points, and option D keeps only outer intervals while incorrectly including the endpoints -1 and 1, where the denominator is zero.