Question

If f(x) =[x] where [x] is greatest integer function then the Domain and Range of [x] ,the value of [-3.7]+[3.7]​

Answer 1

SOLUTION

GIVEN

f(x) =[x]

where [x] is greatest integer function

TO DETERMINE

• Domain and Range of [x] ,

• The value of [-3.7]+[3.7]

EVALUATION

Here the function is given by

$\sf{f(x) = [x] \: \: }$

Where [x] is greatest integer function

[ x ] is the greatest integer but not greater than x

For example,

[ - 2.5 ] = - 3

[ 2.5 ] = 2

DOMAIN

Here the function is well defined for every Real values of x

So the domain of the function is Set of Real numbers

$\sf{Hence \: Domain \: of \: the \: function \: = \: \mathbb{R}}$

RANGE

Here for any Real number x,

[ x ] is an integer

$\therefore \sf{ \: f(x) \in \mathbb{Z} \: \: for \: every \: \: x \in \mathbb{R} \: }$

Hence Range of the function is the Set of Integers

$\sf{Hence \: Range \: of \: the function = \: \mathbb{Z}}$

CALCULATION FOR [-3.7] + [3.7]

Here by the definition of [ x]

$\sf{[ - 3.7 \: ] = - 4}$

$\sf{[ 3.7 \: ] = 3}$

Hence

$\sf{[ - 3.7 \: ] + [ 3.7 \: ]\: }$

$= \sf{ - 4 + 3 \: }$

$\sf{ = - 1}$

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LEARN MORE FROM BRAINLY

Let f be a function whose domain is the set of all real number.if f(x) =|x|-x, what is the range of f

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