Functions Question 615
Question: If $ f(x+ay,\ x-ay)=axy $ , then $ f(x,\ y) $ is equal to
[AMU 2001]
Options:
A) xy
B) $ x^{2}-a^{2}y^{2} $
C) $ \frac{x^{2}-y^{2}}{4} $
D) $ \frac{x^{2}-y^{2}}{a^{2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ f(x+ay,,x-ay)=axy $ ?..(i) Let $ x+ay=u $ and $ x-ay=v $ Then $ x=\frac{u+v}{2} $ and $ y=\frac{u-v}{2a} $ Substituting the value of x and y in (i), we obtain $ f(u,v)=\frac{u^{2}-v^{2}}{4} $
Þ $ f(x,,y)=\frac{x^{2}-y^{2}}{4} $ .
BETA
