Question

The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is ______.

Options

• (2, 3]

• [2, 3)

• (2, 3)

• [2, 3]

Answer 1

The domain of the real valued function f(x) = `sqrt((x - 2)/(3 - x))` is [2, 3).

Explanation:

We have,

f(x) = `sqrt((x - 2)/(3 - x))`

Clearly, f(x) will be defined when

3 - x > 0 ⇒ x < 3

and x - 2 ≥ 0 ⇒ x ≥ 2

∴ Domain of f(x) is [2, 3).