The function f(x) is defined for all real x. If `f(a+b)=f(ab) AA a " a – InterviewSolution

1.	The function f(x) is defined for all real x. If `f(a+b)=f(ab) AA a " and " b " and " f(-(1)/(2))=-(1)/(2)` then find the value of `f(1005).`
Answer» We have `(f(a+b)=f(ab) AA a " and " b` Put ` a=0` ` :. f(b)=f(0)=k ` (say) Putting `b=0` in given relation, `f(a)=f(0)=k` Thus `f(a)=f(b)=k AA a,b` Hence, `f(x)` is a constant function. ` :. f(1005)=f(-(1)/(2))` `=-(1)/(2)`

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