Write the domain of the real function f(x)= x-[x] . - Vidyadip

Question

Write the domain of the real function $\text{f(x)}=\sqrt{\text{x}-[\text{x}]}.$

✓

Answer

We have, $\text{f(x)}=\sqrt{\text{x}-[\text{x}]}$
The domain of will be real only if
$\text{x}-[\text{x}]\geq0$
⇒ Domain of f = x for all $\text{x}\in\text{R}$
$\therefore$ Domain of f = R
$[\because\ \text{f(x)}=\text{x}-[\text{x}]=\text{x}\ \forall\ \text{x}\in\text{R}]$

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