Question

if f(x+y,x-y) = 3x + 5y, find f(x,y)

Answer 1

Answer: $f(x,y)=4x-y$

Step-by-step explanation: Let u,v be

$u=x+y \qquad;\qquad v=x-y$

adding both equations

$u+v=2x\Longrightarrow x=\dfrac{u+v}{2}$

replacing and solving for y we get   $y=\dfrac{u-v}{2}$

So now

$f(u,v)=3\left(\dfrac{u+v}{2}\right)+5\left(\dfrac{u-v}{2}\right)=\dfrac{8u-2v}{2}=4u-v$

Then we can conclude that $f(x,y)=4x-y$

Answer 2

Answer: f(x, y) = 4x - y

Step-by-step explanation: Let u,v be

u = x + y ; v = x - y

adding both equations

u + v = 2x ⇒ x = u + v

2

replacing and solving for y we get

y = u - v

2

So now

f(u, v) = 3(u + v) + 5(u - v)

2 2

= (8u - 2v)

2

= 4u - v

Then we can conclude that f(x, y) = 4x - y

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