Let $\mathrm{f}$ be a function defined by $\mathrm{f}(\mathrm{xy})=\frac{f(x)}{y}$ for all positive real…
Let $\mathrm{f}$ be a function defined by $\mathrm{f}(\mathrm{xy})=\frac{f(x)}{y}$ for all positive real numbers $x$ and $y$. If $f(30)=20$, then $f(40)=$
10
15
25
17
Solution
A function $\mathrm{f}$ is defined as
$
\begin{aligned}
& f(x y)=\frac{f(x)}{y}, x>0, y>0 \\
& \text { and } f(30)=20 \\
& \Rightarrow f(40)=f\left(30 \cdot \frac{4}{3}\right)=f(30) \cdot \frac{3}{4}=20 \cdot \frac{3}{4}=15
\end{aligned}
$