A) At least one root in \[[0,\,1]\]
B) At most one root in \[[0,\,1]\]
C) Exactly one root in \[[0,\,1]\]
D) No root in \[[0,\,1]\]
Correct Answer: A
Solution :
[a] Consider \[h(x)=f(x)-f(x+1)\] \[h(0)=f(0)-f(1)\] \[h(1)=f(1)-f(2)=f(1)-f(0)\] [Given \[f(0)=f(2)\]] i.e., \[h(0)\] and \[h(1)\] are of opposite signs and \[h(x)\] is continuous function. Hence, \[h(x)\] will have at least one root in \[(0,\,\,1)\] or \[[0,\,\,1]\].You need to login to perform this action.
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