Question

The range of the function f(x) = `""^(7 - x)P_(x - 3)` is ______.

Options

• {1, 2, 3, 4, 5}

• {1, 2, 3, 4, 5, 6}

• {1, 2, 3, 4}

• {1, 2, 3}

Answer 1

The range of the function f(x) = `""^(7 - x)P_(x - 3)` is {1, 2, 3}.

Explanation:

Here, `""^(7 - x)P_(x - 3)` is defined if 7 – x ≥ 0, x – 3 ≥ 0

and 7 – x ≥ x – 3

`\implies` 3 ≤ x ≤ 5 and x ∈ I

∴ x = 3, 4, 5

∴ f(3) = `""^(7 - 3)P_(3 - 3)` = ⁴P₀ = 1

∴ f(4) = `""^(7 - 4)P_(4 - 3)` = ³P₁ = 3

∴ f(5) = `""^(7 - 5)P_(5 - 3)` = ²P₂ = 2

Hence, range of f(x) = {1, 2, 3}