Functional Equation

Algebra Level 3

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

For more problems try my set


The answer is 15.

Akshay Sharma by Akshay Sharma , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Akshay Sharma
Mar 16, 2016

Since f ( x y ) = f ( x ) y f(xy)=\frac{f(x)}{y}
f ( 30 ) = 20 f(30)=20
s u b s t i t u t i n g substituting x = 30 , y = 4 3 x=30,y=\frac{4}{3}
f ( 30 × 4 3 ) = 20 4 3 f(30\times\frac{4}{3})=\frac{20}{\frac{4}{3}}
f ( 40 ) = 15 f(40)=15


4 Helpful 0 Interesting 0 Brilliant 0 Confused
Umair Siddiqui
Mar 16, 2016

f (30) = f ( 5× 6) = f (5) / 6 

     20 = f (5) / 6
  f (5) = 20 × 6

f (40) = f ( 5 × 8) = f (5) / 8 = 20×6/8 = 15

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...