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 $\text{Range(f)}=\phi$

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

Explore more

More "(Each question 1 marks)" from Functions→Functions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Determine the contrapositive of the following statements: If it snows, then they do not drive the car.

Find the derivative of function $f(x) = \cos \left( {x - \frac{\pi }{8}} \right)$ from first principle.

In a $\triangle\text{ABC},$ if $\sin\text{A}$ and $\sin\text{B}$ are the roots of the equation $\text{c}^2\text{x}^2-\text{c(a + b) x + ab}=0,$ then find $\angle\text{C}.$

If $\text{f(x)}=\cos\big[\pi^2\big]\text{x}+\cos\big[-\pi^2\big]\text{x},$ where[x] denotes the greatest integer less than or equal to x, then write the value of $\text{f}(\pi)$

In the arithmetic progression whose common difference is non-zero, the sum of first 3n terms is equal to the sum of next n terms. Then the ratio of the sum of the first 2n terms to the next 2n terms is:

$\frac{1}{5}$
$\frac{2}{3}$
$\frac{3}{4}$
None of these

A card is selected from a pack of 52 cards. Calculate the probability that the card is black card.

Write the distance between the vertex and focus of the parabola $y^2+6 y+2 x+5=0$

Write the expression ${^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r-1}}+2\times{^\text{n}}\text{C}_{\text{r}-1}$in the simplest form.

Find the ratio in which the line segment joining the points (2, 4, 5) and (3, −5, 4) is divided by the yz-plane.

List all the elements of the following sets:
$\text{B}=\Big\{\text{x : x}=\frac{1}{\text{2n-1}},1\leq\text{n}\le5\Big\};$