A) \[Z\cup (-\infty ,0)\]
B) \[(-\infty ,0)\]
C) \[Z\]
D) R
Correct Answer: D
Solution :
[d] \[g(f(x))=g(\left| x \right|)=[\left| x \right|];\] \[f(g(x))=f([x])=\left| [x] \right|\] When \[x\ge 0,[\left| x \right|]=[x]=\left| [x] \right|\] \[\therefore \,\,\,f(g(x))=g(f(x))\] When \[x<0,[x]\le x<0\Rightarrow \left| [x] \right|\ge \left| x \right|\] \[\therefore \left| [x] \right|\ge \left| x \right|\ge [\left| x \right|]\] \[\Rightarrow f(g(x))\ge g(f(x))\] Thus, \[g(f(x))\le f(f(x))\] for all \[x\in R\]You need to login to perform this action.
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