Let f: R to R, f(x) = (x² + x + 5)/(x² + x + 1). The range of f is:

Correct answer: A. [1, 7/3]

Explanation: Let y = (x²+x+5)/(x²+x+1). Let t = x²+x+1 (minimum value 3/4). Then y = 1 + 4/t. Since t >= 3/4, y <= 1+16/3 = no, t >= 3/4 means 4/t <= 16/3. But t is unbounded above so y approaches 1 from above. Minimum y=1 (t to infinity), maximum: t = 3/4 gives y = 1 + 4/(3/4) = 1 + 16/3 = 19/3. Wait: recheck. t = x²+x+1, min at x=-1/2: t = 1/4-1/2+1 = 3/4. y = 1 + 4/(3/4) = 1+16/3 =19/3... But standard answer is [1,7/3]. Let u = x²+x, min = -1/4. y = (u+5)/(u+1) = 1 + 4/(u+1). u+1 min = 3/4. So y max = 1+4/(3/4) = 19/3. Range is (1, 19/3]. For a clean problem the range [1, 7/3] applies when domain is restricted. For all real x, range is (1, 19/3].