Relations and Functions — MATHS STD 11 Science — Question

3. {3, 4, 5}

Solution:

The function $\text{f}(\text{x})= ^{7-\text{x}}\text{P}_\text{x-3}$ is defined only if x is an integer satisfying the following inequalities:

$ 7 - \text{x} ≥ 0.....(1)$

$ \text{x} - 3 ≥ 0......(2)$

$ 7 - \text{x} ≥ \text{x} - 3........(3)$

Now, from 1, we get $ \text{x} ≤ 7 ……… (4)$

from 2, we get $\text{x} ≥ 3 ……………. (5)$

and from 2, we get $\text{x} ≤ 5 ………. (6)$

From 4, 5 and 6, we get

$ 3 ≤ \text{x} ≤ 5$

So, the domain is {3, 4, 5}.