JEE Main & Advanced
Sample Paper
JEE Main - Mock Test - 16
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