Question

The function $f\left(x\right)$ is defined for all real x. If $f(a+b)=f\left(ab\right)\forall a$ and $b$ and $f\left(\frac{-1}{2}\right)=\frac{-1}{2},f\left(2007\right)$ equals-

• A. $-2003$
• B. $2003$
• C. $\frac{-1}{2}$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$\frac{-1}{2}$

$f(a+b)=f\left(ab\right)\forall a\&bf\left(\frac{-1}{2}\right)=\frac{-1}{2}tleta=0,weget$

$f(0+b)=f(0\times b)f\left(b\right)=f\left(0\right),$

It shows function is constant.

$\therefore f\left(2007\right)=\frac{-1}{2}$