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Find the domain and range of the real valued function: (iv) f ( x ) = √ x − 3 - Mathematics

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प्रश्न

Find the domain and range of the real valued function:

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

 

उत्तर

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 ( ) = [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, ∞) .

 

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अध्याय 3: Functions - Exercise 3.3 [पृष्ठ १८]

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आरडी शर्मा Mathematics [English] Class 11
अध्याय 3 Functions
Exercise 3.3 | Q 3.04 | पृष्ठ १८

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