2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Functions

JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relation and Functions-II

  • question_answer
    If \[f:R\to R\] and \[g:R\to R\] are given by \[f(x)=\left| x \right|\] and \[g(x)=[x]\] for each \[x\in R,\] then \[[x\in R:g(f(x))\le f(g(x))\}=\]

    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.
You will be redirected in 3 sec spinner