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
$[\because\ \text{f(x)}=\text{x}-[\text{x}]=\text{x}\ \forall\ \text{x}\in\text{R}]$
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
$[\because\ \text{f(x)}=\text{x}-[\text{x}]=\text{x}\ \forall\ \text{x}\in\text{R}]$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Give an alternative arrangement for the following circuit, so that the new circuit has minimum switches.
Evaluate :
→$\int_2^3 \frac{1}{x^2+5 x+6} \cdot d x$
Find the matrix of co-factors for the matrix $\left[\begin{array}{cc}1 & 3 \\ 4 & -1\end{array}\right]$
→Diffrentiate the following w. r. t. x
→$\cos ^{-1}\left(3 x-4 x^3\right)$
If two non-zero vectors $\bar{a}$ and $\bar{b}$ are collinear then prove that there exist scalars $m$ and $n$ such that $m \bar{a}+n \bar{b}=\overline{0}$ and $(m, n) \neq(0,0)$.
→Given an interval $[a, b]$ that satisfies hypothesis of Rolle's theorem for the function $f(x)=x^3-2 x^2+3$. It is known that $a=0$. Find the value of $b$.
→Find the value of x, if:
$\begin{vmatrix}3&\text{x}\\\text{x}&1\end{vmatrix}=\begin{vmatrix}3&2\\4&1\end{vmatrix}$
→$\begin{vmatrix}3&\text{x}\\\text{x}&1\end{vmatrix}=\begin{vmatrix}3&2\\4&1\end{vmatrix}$
Find the general solutions of the following equations :
→$\tan ^2 \theta=3$
Prove that $2(\bar{a}-\bar{b}) \times 2(\bar{a}+\bar{b})=8(\bar{a} \times \bar{b})$
→Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency. [~(~p ∧ ~q)] ∨ q