Multiple choice general knowledge math & puzzles

The range of f(x) = x2 -2x + 1 is given by the interval

  1. [0 , +infinity)

  2. (-infinity , 1]

  3. (0 , + infinity)

  4. (1 , + infinity)
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A Correct answer
Explanation

The function f(x) = x² - 2x + 1 can be written as f(x) = (x-1)² by completing the square. Since any squared quantity is always non-negative, (x-1)² ≥ 0 for all real x. Therefore, the range of f(x) is [0, +∞), meaning all values from 0 to positive infinity, including 0 (when x = 1). Option C is incorrect because it excludes 0, which is achieved at x = 1. Option B incorrectly suggests the function is bounded above, but parabolas opening upward are unbounded. Option D excludes 0 and incorrectly shifts the starting point.

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