Question

If a derivable function $f : R ^{+} \rightarrow R$ satisfies $f ( xy )= f ( x )+ f ( y ) \quad \forall x , y \in R ^{+}$. If $f (16)=3$ then $\frac{1}{ f (2)}+\frac{1}{ f (4)}$ is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

$\Theta f(x y)=f(x)+f(y)$
$\Rightarrow f (16)= f (4)+ f (4)=3 \Rightarrow f (4)=\frac{3}{2} $
$\Rightarrow f (2)+ f (2)=\frac{3}{2} \Rightarrow f (2)=\frac{3}{4} $
$\therefore \frac{1}{ f (2)}+\frac{1}{ f (4)}=\frac{4}{3}+\frac{2}{3}=2 $