Question

Let $f$ be a function satisfying $f( xy )=\frac{ f ( x )}{ y }$ for all positive real numbers $x$ and $y$. If $f(30)=20$, then the value of $f(40)$ is

• A. 15
• B. 20
• C. 40
• D. 60

Answer 1

Answer: (A)

An equation of this kind is called a functional equation, and can often be solved by choosing particular values for the variables. In this case, by choosing $x=1$, we see that $f(y)=\frac{f(1)}{y}$ for all y. put $y$
$=30 ; f (1)=30 \cdot f (30)=30 \cdot 20=600$
$. \text { Now } f(40)=\frac{ f (1)}{40}=\frac{600}{40}=15$