question_answer

Let \[g(x)=1+x-[x],[x]\]is the greatest integer not greater than x. If  then for all x, f(g(x)) equals

A) x         

B)        1     

C) f(x)  

D) g(x)

Correct Answer: B

Solution :

[b]: The given functions are \[g(x)=1+x-[x]\] and We see that \[g(x)=1+x-[x]=1+(x-[x])\] \[=1+\{c\}\ge 1(\because 0\le \{x\}<1)\] \[\therefore \]\[f(g(x))=1\]for all x