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  • Find the range of f(x) = x-[x]/1+x-[x], where [ .] denotes greatest integer function.

Find the range of f(x) = x-[x]/1+x-[x], where [ .] denotes greatest integer function.

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Solution:

y=x-[x]/1+x-[x] =x/1+x

⇒   1/y=1/x +1

⇒    1/x =1-y/y

⇒    x=y/1-y

\ Rightarrow 0leq y/1-y< 1\ \ Rightarrow Rnage=[0,1/2)

Posted by

Deependra Verma

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