Write the domain and range of f(x)= x-[x] - Vidyadip

Question

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

✓

Answer

We have,
$\text{f(x)}=\sqrt{\text{x}-[\text{x}]}$
we know that $0\leq\text{x}-[\text{x}]<1$ for all $\text{x}\in\text{R}$
$\Rightarrow\ \text{f(x)}=\sqrt{\text{x}-[\text{x}]}$ is defined for all $\text{x}\in\text{R}$
$\therefore\ \text{Domain(f)}=\text{R}$
and Range (f) = [0, 1)

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