Question

Assertion(A): The domain of the function $f\left(x\right)=\sqrt{x-\left[x\right]}$ is R.
Reason (R): The domain of the function $\sqrt{f\left(x\right)}$ is $\{x:f(x)\ge 0\}$

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

Answer: (A)

Both A and R are true and R is the correct explanation of A

$\sqrt{f\left(x\right)}$ is defined only for $f\left(x\right)\ge 0$
$\therefore$ it's domain is $x:f\left(x\right)\ge 0$
For $f\left(x\right)=\sqrt{x-\left[x\right]}$
$x-\left[x\right]\ge 0$
$\Rightarrow x\ge \left[x\right]$
$x$ is always greater than $\left[x\right]$
$\therefore$ it's domain is R