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

Question

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

✓

Answer

We know,
$\text{f(x)}=\sqrt{[\text{x}]-\text{x}}$
We know that $-1<[\text{x}]<-\text{x}\leq0$ for all $\text{x}\in\text{R}$
$\Rightarrow\sqrt{[\text{x}]-\text{x}}$ is not defined for all $\text{x}\in\text{R}$
$\therefore\ \text{Domain(f)}=\phi$
and $\text{Range(f)}=\phi$

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