Question

lf $f\left(x\right)=f\left(xy\right),\forall x,y\in R$ and $f\left(2005\right)=2005$ then $f(-2005)=$

• A. $2005$
• B. $-2005$
• C. $0$
• D. $1$

Answer 1

The correct option is A $2005$

$f\left(x\right)=f\left(xy\right)$
Substitute $y=-1$
$f\left(x\right)=f(-x)$
$\because f\left(2005\right)=2005$
$\therefore f(-2005)=f\left(2005\right)$
$=2005$