Math Help - functions

1. functions

if f(x+2y,x-2y)=xy then f(x,y)=

2. Originally Posted by prasum
if f(x+2y,x-2y)=xy then f(x,y)=

Hint

Use the substitution $u=x+2y,v=x-2y$ .

3. Originally Posted by FernandoRevilla
Hint

Use the substitution $u=x+2y,v=x-2y$ .
can yu please explain me the method

4. Solving, $x=(u+v)/2,\;y=(u-v)/4$ so,

$f(u,v)=xy=\dfrac{u+v}{2}\cdot \dfrac{u-v}{4}=\dfrac{u^2-v^2}{8}$

Now, change the name of the variables, $u$ by $x$ and $v$ by $y$.

5. Originally Posted by prasum
can yu please explain me the method
You were told to let u= x+ 2y, v= x- 2y. The point of that is that f(x+ 2y, x- 2y)= xy becomes f(u, v)= xy. Now you want to write xy in terms of u and v. Can you solve u= x+ 2y and v= x- 2y for x and y in terms of u and v?