A) A linear function of x
B) An exponential function of x
C) A constant function
D) None of these
Correct Answer: C
Solution :
given, \[\,f(x)+f(x+6)=f(x+3)+f(x+9)\] |
Put \[x=x+3\] |
\[f(x+3)+f(x+9)=f(x+6)+f(x+12)\] |
\[\Rightarrow \]\[f(x)=f(x+12)\] |
Let \[g,(x)=\int\limits_{x}^{x+12}{f(t)dt}\] |
\[\Rightarrow \]\[g'(x)=f(x+12)-f(x)=0\] |
\[\Rightarrow \]\[g(x)\]is a constant function. |
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