First slide

Algebra of real valued functions

Question

If f(x+ay,x-ay)=axy,then f(x,y)is equal to

Easy

A

xy
B

x-²a²y²
C

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

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

Solution

Given
f(x+ay,x-ay)=axy
Let x+ay=t……(i)
and x-ay=u……(ii)
On solving i & ii we get
x= $\frac{t + u}{2}$ and $y = \frac{t - u}{2 a}$ $∴$ f(t,u)=a $\frac{t + u}{2}$ *( $\frac{t - u}{2 a}$ )
$\Rightarrow$ f(t,u)= $\frac{t^{2} - u^{2}}{4}$
$∴$ f(x,y)= $\frac{x^{2} - y^{2}}{4^{}}$

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