If f(x)=(2x-5)/(x+4), what is the range of f?

Correct answer: R\{2}

Let y=(2x−5)/(x+4), where x≠−4 because the original denominator cannot be zero. To determine which y-values are possible, solve for x: y(x+4)=2x−5, so yx+4y=2x−5 and x(y−2)=−5−4y. Hence x=(−5−4y)/(y−2), provided y≠2. For every real y other than 2, this formula gives a real x, and that x is not −4; substituting x=−4 into the rearranged equation would produce a contradiction. The value y=2 is impossible because it would require 2(x+4)=2x−5, giving 8=−5. Thus the only excluded output is 2, and the range is R\{2}. Option A is correct. Option B confuses an excluded domain value with an excluded range value; C and D have no valid algebraic basis.