Question

Find the domain and range of the real valued function:

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

 

Answer 1

Given:

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

Domain ( f ) : Clearly, f (x) assumes real values if x -3 ≥ 0 ⇒ x ≥ 3 ⇒ x ∈ [3, ∞) .
Hence, domain ( f ) = [3, ∞)
Range of f : For x ≥  3, we have:
x-3 ≥ 0

\[\Rightarrow \sqrt{x - 3} \geq 0\]

⇒ f (x) ≥ 0
Thus, f (x) takes all real values greater than zero.
Hence, range (f) = [0, ∞) .