$Let f (x) = \frac{x - [x]}{1 + x - [x]}, x ϵ R, [] dentoes the greatest integer function . Then, the range of f is$

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Solution

The correct option is 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

$x \Rightarrow [x] as x tends to an integer. A s \to 1, \frac{x}{1 + x} \to \frac{1}{2} Hence , the range of f (x) i s [0, \frac{1}{2})$

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$L e t f (x) = \frac{x - [x]}{1 + x - [x]}, x ϵ R, [] d e n t o e s t h e g r e a t e s t i n t e g e r f u n c t i o n . T h e n, t h e r a n g e o f f i s$

Q. 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

Q. 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

Q. 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

The range of f(x) = $\frac{x - [x]}{1 + x - [x]}$ where [] represents greatest integer function.

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Let f(x)=x−[x]1+x−[x],xϵ R, [ ]dentoes the greatest integer function.Then, the range of f is

The correct option is 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⇒[x]as x tends to an integer.As →1,x1+x→12Hence , the range off(x) is[0,12)

$Let f (x) = \frac{x - [x]}{1 + x - [x]}, x ϵ R, [] dentoes the greatest integer function . Then, the range of f is$

The correct option is 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

$x \Rightarrow [x] as x tends to an integer. A s \to 1, \frac{x}{1 + x} \to \frac{1}{2} Hence , the range of f (x) i s [0, \frac{1}{2})$