Let f(x)=x−[x]1+x−[x],x ϵ R, where [ x] denotes the greatest integer func

Question

Let

f (x) = \frac{x - [x]}{1 + x - [x]}, x ϵ R

, where [ x] denotes the greatest integer function. Then, the range of f is

Options:

A . (0,1)

B . [0,12)

C . [0,1]

D . [0,12]

Answer: Option B
:
B
The graph of

y = x - [x]

is as shown below

When x is an integer,

x - [x] = 0

Hence, f(x) = 0 when x is an integer

x \to [x]

as x tends to an integer.
Let X =

x - [x]

So,

f (x) = \frac{X}{1 + X}, X ϵ [0, 1)

X \to 1, \frac{X}{1 + X} \to \frac{1}{2}

Hence, the range of f(x) is

[0, \frac{1}{2})

Was this answer helpful ?

Next Question

More Questions on This Topic :

Question 1. The period of the function |sinx|+|cosx| is ....

Question 2. Range of f(x)=tan(π[x2−x])1+sin(cos x) is (where [x] denotes the greatest integer function) ....

Question 3. With reference to a universal set, the inclusion of a subset in another, is relation, which is....

Question 4. R is relation over the set of integers and it is given by (x, y) ϵ R ⇔ R |x - y| ≤ 1. Th....⇔ R |x - y| ≤ 1. Then, R is

Question 5. The range of the function f(x)=cos2x4+sinx4,x ϵ R is....

Question 6. F(x)=x2−3x+4x2+3x+4 the range of f(x) is ....

Question 7. Let P = {(x,y) x2+y2=1,x,y∈R}. Then P is.....

Question 8. Let R be a relation over the set N×n and it is defined by (a, b) R (c, d) ⇒ a+ d = b + c. Then, ....⇒ a+ d = b + c. Then, R is

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0