question_answer

The graph of the function \[y=f(x)\] is symmetrical about the line \[x=2,\] then

A) \[f(x)=-f(-x)\]

B) \[f(2+x)=f(2-x)\]

C) \[f(x)=f(-x)\]

D) \[f(x+2)=f(x-2)\]

Correct Answer: B

Solution :

[b] Let us consider a graph symmetric with respect to line x = 2 as shown in the figure. From the figure \[f({{x}_{1}})=f({{x}_{2}}),\] where \[{{x}_{1}}=2-x\] and \[{{x}_{2}}=2+x\] \[\therefore f(2-x)=f(2+x)\]