Question
Find the domain of $\text{f(x)}=\cot\text{x}+\cot^{-1}\text{x}$

Answer

Domain of $\cot\text{x}$ is $(0,\pi)$
Domain of $\cot^{-1}\text{x}$ is R.
So domain of $\cot\text{x}+\cot^{-1}\text{x}$ is R.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $\vec{\text{r}}=\text{x}\hat{\text{i}}+\text{y}\hat{\text{j}}+\text{z}\hat{\text{k}},$ then write the value of $\big|\vec{\text{r}}\times\hat{\text{i}}\big|^2.$
Find the equation of the line in cartesian form that passes through the point with position vector $2\hat i - \hat j + 4\hat k$ and is in the direction $\hat i + 2\hat j - \hat k$.
Determine whether or not the definition of  $*$ given below gives a binary operation. In the event that $*$ is not a binary operation give justification of this.
On $Z^+,$ defined $*$ by $a * b = a - b.$
Here, $Z^+$ denotes the set of all non$-$negative integers.
If the vectors $3\hat{\text{i}}-2\hat{\text{j}}-4\hat{\text{k}}$ and $18\hat{\text{i}}-12\hat{\text{j}}-\text{m}\hat{\text{k}}$ are parallel,  find the value of m.
Evaluate the definite integral in Exercise:
$\int\limits_{-1}^{1}\text{(x}+1)\ \text{dx}$
A die is tossed thrice. Find the probability of getting an odd number at least once.
For the principal value, evaluate $\cot \left[\sin ^{-1}\left\{\cos \left(\tan ^{-1} 1\right)\right\}\right]$
Integrate the function in exercise.
$\text{x} \ \sin3\text{x}$
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors of the same magnitude inclined at an angle of $60^\circ$ such that $\vec{\text{a}}.\vec{\text{b}}=8,$ write the value of their magnitude.
Verify that the function $y=x \sin 3 x$ (implicit or explicit) is a solution of the differential equation $\frac{d^{2} y}{d x^{2}}+9 y-6 \cos 3 x=0$