If f x -2 y - x -2 y - xy- then f x - y equalsA- x2-y2-22B- x2-y2-x2-u2D- x2-y2-x2-y22

The correct option is A Let x + 2y = p x – 2y = q Solving we got x=p+q/2 y=p q/2 ∴ f(p,q)=p^2 q^2/8 F(x, y)=x^2 y^2/8 ...

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Standard XII

Mathematics

Definition of Functions

If f x +2 y ,...

Question

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

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Solution

The correct option is A
Let x + 2y = p
x – 2y = q
Solving we got $x = \frac{p + q}{2}$
$y = \frac{p - q}{2} ∴ f (p, q) = \frac{p^{2} - q^{2}}{8} F (x, y) = \frac{x^{2} - y^{2}}{8}$

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

The correct option is A Let x + 2y = p x – 2y = q Solving we got x=p+q2 y=p−q2∴f(p,q)=p2−q28F(x,y)=x2−y28

The correct option is A
Let x + 2y = p
x – 2y = q
Solving we got $x = \frac{p + q}{2}$
$y = \frac{p - q}{2} ∴ f (p, q) = \frac{p^{2} - q^{2}}{8} F (x, y) = \frac{x^{2} - y^{2}}{8}$