Question

The domain of the function f(x) = `""^(24 - x)C_(3x - 1) + ""^(40 - 6x)C_(8x - 10)` is

Options

• {2, 3}

• {1, 2, 3}

• {1, 2, 3, 4}

• None of these

Answer 1

{2, 3}

Explanation:

`""^(24 - x)C_(3x - 1)` is defined if, 

`24 - x > 0, 3x - 1 ≥ 0` and `24 - x ≥ 3x - 1`

⇒ `x < 24, x ≥ 1/3` and `x ≤ 25/4`

⇒ `1/3 ≤ x ≤ 25/4`

`""^(40 - 6x)C_(8x - 10)` is defined if,

`40 - 6x > 0, 8x - 10 ≥ 0` and `40 - 6x ≥ 8x - 10`

⇒ `x < 20/3, x ≥ 5/4` and `x ≤ 25/7`

⇒ `5/4 ≤ x ≤ 25/7`

From (1) and (2), we get `5/4 ≤ x ≤ 25/7`

But 24 – x ∈ N

∴ x must be an integer, x = 2, 3.

Hence domain (f) = {2, 3}.