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  4. Let f be a function such that f(x y)=(f(x)/y) for all positive real numbers x, y . If f(20)=15, then f(50)=

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Q. Let $f$ be a function such that $f(x y)=\frac{f(x)}{y}$ for all positive real numbers $x, y .$ If $f(20)=15$, then $f(50)=$

AP EAMCETAP EAMCET 2019

Solution:

Given, $f(x y)=\frac{f(x)}{y}$ and $f(20)=15$
$\Rightarrow f(5 \times 4)=\frac{f(5)}{4}=15$
$\Rightarrow f(5)=4 \times 15=60$
Now, $ f(50)=f(5 \times 10)=\frac{f(5)}{10}=\frac{60}{10}=6$