Question

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

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

 

Answer 1

(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) .