If f x -2 y - x -2 y - xy- then f x - y equalsA- x2-y2-4B- x2-y2-8C- x2-y2-2D- x2-y2-4

The correct option is B x^2 y^28f(x + 2y, x 2y) = xy ⋯(1) Put x + 2y = u and x 2y = v ⇒ x = u+v2 ⇒ y = u v4 Putting x and y in (1), we get f(u, v) = ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Definition of Functions

If f x +2 y ,...

Question

If $f (x + 2 y, x - 2 y) = x y,$ then $f (x, y)$ equals

\frac{x^{2} - y^{2}}{8}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{x^{2} - y^{2}}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{x^{2} + y^{2}}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{x^{2} - y^{2}}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{x^{2} - y^{2}}{8}$
$f (x + 2 y, x - 2 y) = x y \dots (1)$
Put $x + 2 y = u$ and $x - 2 y = v$
$\Rightarrow x = \frac{u + v}{2} \Rightarrow y = \frac{u - v}{4}$
Putting $x$ and $y$ in $(1),$ we get
$f (u, v) = \frac{u^{2} - v^{2}}{8} ∴ f (x, y) = \frac{x^{2} - y^{2}}{8}$

Suggest Corrections

Similar questions

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

Q. If f(x+2y, x-2y)=xy, then f(x, y) equals

Let $f (x, y) = \sqrt{x^{2} + y^{2}} + \sqrt{x^{2} + y^{2} - 2 x + 1} + \sqrt{x^{2} + y^{2} - 2 y + 1} + \sqrt{x^{2} + y^{2} - 6 x - 8 y + 25} \forall x, y ϵ R, t h e n$

Q. The equation of the circle passing through points of intersection of the circle

x^{2} + y^{2} - 2 x - 4 y + 4 = 0

and the line

x + 2 y = 4

and touches the line

x + 2 y = 0

, is

Q. If

\frac{3 x + 2 y}{3 x - 2 y} = \frac{4}{3}

then find the value of

\frac{x^{2} + y^{2}}{x^{2} - y^{2}}

Join BYJU'S Learning Program

If f(x+2y,x−2y)=xy, then f(x,y) equals

The correct option is A x2−y28f(x+2y,x−2y)=xy ⋯(1) Put x+2y=u and x−2y=v ⇒x=u+v2⇒y=u−v4 Putting x and y in (1), we get f(u,v)=u2−v28∴f(x,y)=x2−y28

If $f (x + 2 y, x - 2 y) = x y,$ then $f (x, y)$ equals