If $ f(x+a y, x-a y)=a x y $, then $ f(x, y) $ is equal to

JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Application +4 | -1

f(x+a y, x-a y)=a x y

, then

f(x, y)

is equal to

View answer and explanation

Correct option: C

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

Option C (

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

) is correct because by substituting

u = x+ay

and

v = x-ay

and solving for x and y, then substituting into the original equation, we get

f(x, y) = \frac{{x^{2}-y^{2}}}{{4}}

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