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)

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 "1 Marks Question" from Functions→Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

State the converse and contrapositive of the following statements:
A positive integer is prime only if it has no divisors other than 1 and itself.

Translate the following statement into symbolic form:
Students can take Hindi or English as an optional paper.

Check whether the probabilities P(A) and P(B) are consistently defined P(A) = 0.5, P(B) = 0.4, $P(A \cup B) = 0.8$

Write down the all possible subset of the given set.
$\{a\}.$

Identify the Quantifiers in the following statement:
There exists a triangle which is not an isosceles triangle.

Write down the converse of following statement:
If today is Monday, then tomorrow is Tuesday.

If $p(n): 2 \times 4^{2n-1} + 3^{3n+1} $ is divisible by $\lambda$ for all $\text{n}\in\text{N}$ is true, then find the value of $\lambda$

For the following statements, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
To entry a country, you need a passport or a voter registration card.

If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find $A \cap C \cap D$

Write the length of the intercept made by the circle $x^2 + y^2 + 2x - 4y - 5 = 0$ on y-axis.