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# Write the Domain and Range of F ( X ) = √ X − [ X ] . - CBSE (Science) Class 11 - Mathematics

#### Question

Write the domain and range of  $f\left( x \right) = \sqrt{x - \left[ x \right]}$ .

#### Solution

$f\left( x \right) = \sqrt{x - \left[ x \right]}$
$\text{ Since f(x) is defined for all values of } x, x \in R .$
$\text{ Or dom } (f(x)) = R$
$\text{ Since, x - [x] = {x}, which is the fractional part of any real number } x,$
$f(x) = \sqrt{{x}} . . . . . (1)$
$\text{ We know that }$
$0 \leq {x} < 1$
$\Rightarrow \sqrt{0} \leq \sqrt{{x}} < \sqrt{1}$
$\Rightarrow 0 \leq f(x) < 1 { \text{ from } (1)}$
$\text{ Thus, range of f(x) is } [0, 1) .$

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#### APPEARS IN

RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 3: Functions
Ex.3.50 | Q: 13 | Page no. 42
Solution Write the Domain and Range of F ( X ) = √ X − [ X ] . Concept: Functions.
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