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📐 Mathematics  ·  Relations and Functions  ·  JEE

Let f(x) = x² - 4x + 3. Find the set of values of x for which f(x) < 0.

Answer: (1, 3).

  • A (1, 3)
  • B [1, 3]
  • C (-inf, 1)
  • D (3, inf)

Correct answer: A. (1, 3)

Explanation: Factor the quadratic: x²-4x+3 = (x-1)(x-3). Find zeros: x=1 and x=3. Since leading coefficient is positive, parabola opens upward. The product (x-1)(x-3) is negative between the roots: 1 < x < 3. Answer: x ∈ (1, 3)

Concept context

Ordered pairs, Cartesian products, types of relations and functions, domain and range. Foundation for calculus and Class 12 algebra.

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