A) \[f(x)\] is symmetrical about the line \[x=1\]
B) \[g(x)\] is symmetrical about the line \[x=1\]
C) \[f(x)\] is symmetrical about the point \[(1,0)\]
D) \[g(x)\]is symmetrical about the point \[(1,0)\]
Correct Answer: D
Solution :
[d] Given that \[f(x)-g(x)=1\] \[\Rightarrow \,\,\,\,f(x)-1=g(x)\] Also, \[f(2-x)=2-f(x)\] \[\Rightarrow \,\,\,f(2-x)-1=-(f(x)-1)\] \[\Rightarrow \,\,\,\,\,\,\,g(2-x)=-g(x)\] \[\Rightarrow \,\,\,\,\,\,\,g(x)=-g(2-x)\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,g(1+x)=-g(1-x)\] Thus, g is symmetrical about the point\[(1,0)\].You need to login to perform this action.
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