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  • Please help! What is the range of function f(x) = {x}+{-x}

What is the range of function f(x) = {x}+{-x}

  • Option 1)

    [0,1)

  • Option 2)

    (-1,1)

  • Option 3)

    {0,1}

  • Option 4)

    [0,1]

 

Answers (1)

best_answer

As we have learned

Fractional part function -

\left \{ x \right \}=x-\left [ x \right ] \right

When  \left [ x \right ]  Greatest Integer Function

 

- wherein

Range \in \left [\left 0,1 \right ) \right

 

 

 f(x) = {x}+{-x}

If x \epsilon Z f(x) = 0

If x doesn't belong to Z ; then x= Z+k

f(x) = {Z+K}+ {-Z-K}

= K+1-K=1

 

 

 

 

 

 


Option 1)

[0,1)

Option 2)

(-1,1)

Option 3)

{0,1}

Option 4)

[0,1]

Posted by

Himanshu

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