If f:R\rightarrow R and g:R\rightarrow R are defined by f\left( x | Filo
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Class 11

Math

Calculus

Relations and Functions II

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If $$f:R\rightarrow R$$ and $$g:R\rightarrow R$$ are defined by $$f\left( x \right) =x-\left[ x \right]$$ and $$ g\left( x \right) =\left[ x \right]$$  for $$x\in R$$,where $$[x]$$ is the greatest integer not exceeding $$x$$,then for every  $$x\in R$$,$$f(g(x))$$ is equal to

  1. $$x$$
  2. $$0$$
  3. $$f(x)$$
  4. $$g(x)$$
Correct Answer: Option(b)
Solution: $$f(g(x))=[x]-[x]$$
As $$[[x]]=[x]$$
$$fog(x)=[x]-[x]=0$$
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