Let f be a function satisfying f xy - f x -y for all positive real numbers x and y- If f 30 - 20- then the value of f 40 is

The correct option is A 15 Put x= 30 , y= 40 30 nbsp; then nbsp; f( 30× 40 30 nbsp;) = f( 30 ) nbsp; 40 × 30 Hence, f(4 ...

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Standard XII

Physics

Logic Gates

Let f be a ...

Question

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

15

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40

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Solution

The correct option is A $15$
Put $x = 30$ , $y = \frac{40}{30}$ then
$f (30 \times \frac{40}{30}) = \frac{f (30)}{40} \times 30$
Hence,
$f (40) = 15$

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

The correct option is A 15Put x=30, y=4030 then f(30×4030)=f(30)40×30Hence,f(40)=15

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

The correct option is A $15$
Put $x = 30$ , $y = \frac{40}{30}$ then
$f (30 \times \frac{40}{30}) = \frac{f (30)}{40} \times 30$
Hence,
$f (40) = 15$