#### Question

Find the domain of the real valued function of real variable:

(iv) \[f\left( x \right) = \frac{\sqrt{x - 2}}{3 - x}\]

#### Solution

(iv) Given:

\[f\left( x \right) = \sqrt{\frac{x - 2}{3 - x}}\]

Clearly, *f *(*x*) assumes real values if*x -2 ≥* 0 and 3-*x* > 0

⇒ *x* ≥ 2 and 3 > *x*

⇒ *x* ∈ [2, 3)

Hence, domain ( *f* ) = [2, 3) .

Is there an error in this question or solution?

Solution Find the Domain of the Real Valued Function of Real Variable: (Iv) F ( X ) = √ X − 2 3 − X Concept: Cartesian Product of Sets.