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COMEDK · Maths · 4. Permutation Combination

The range of the function \(f(x) = {}^{(7-x)}P_{(x-3)}\) is

  1. A \(\{1, 2, 3, 4\}\)
  2. B \(\{1, 2, 3, 4, 5\}\)
  3. C \(\{1, 2, 3\}\)
  4. D \(\{1, 2, 3, 4, 5, 6\}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\{1, 2, 3\}\)

Step-by-step Solution

Detailed explanation

For \(f(x) = {}^{(7-x)}P_{(x-3)}\) to be defined, the following conditions must be satisfied: \(7 - x \ge 0 \Rightarrow x \le 7\) \(x - 3 \ge 0 \Rightarrow x \ge 3\) \(7 - x \ge x - 3 \Rightarrow 2x \le 10 \Rightarrow x \le 5\) Also, \(x\) must be an integer. From the above…