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VIT Engineering VIT Engineering Solved Paper-2010

  • question_answer
    If \[F\] is functions such that \[F(0)=2,\]\[F(1)=3,\]\[F(x+2)=2F(x)-F(x+1)\] for \[x\ge 0,\] than\[F(5)\] is equal to

    A)  -7

    B)  -3

    C)  17

    D)  13

    Correct Answer: D

    Solution :

    We have, \[F(x+2)=2F(x)-F(x+1)\] ?(i) Putting \[x=0,\]we get \[F(2)=2F(0)-F(1)\] \[\Rightarrow \] \[F(2)=2(2)-3\]   \[\{\because \,F(0)=2,\,F(1)=3\}\] \[\Rightarrow \] \[F(2)=4-3\] \[\Rightarrow \] \[F(2)=1\] Putting \[x=1,\] in Eq. (i) we get \[F(3)=2F(1)-F(2)\]          \[=2(3)-1\] \[\{\because F(1)=3,\,F(2)=1\}\] \[\Rightarrow \] \[F(3)=5\] Putting \[x=2,\]in Eq. (i) we get \[F(4)=2F(2)-F(3)\]           \[=2(1)-5\] \[\{\because F(2)=1,\,F(3)=5\}\] \[F(4)=-3\] Putting \[x=3,\]in Eq. (i), we get \[F(5)=2F(3)-F(4)\]          \[=2(5)+3\]\[\{\because F(3)=5,\,F(4)=-3\}\] \[\Rightarrow \] \[F(5)=13\]


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