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Question

If a non-zero function f satisfies the relation f(x+y)+f(xy)=2f(x).f(y) for all x,y in R and f(0)0; then f(10)f(10)=


A
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Solution

The correct option is B 0
Given, f(x+y)+f(xy)=2f(x)f(y)

Put y=0,x=x
f(x)+f(x)=2f(x)f(0)
2f(x)=2f(x)f(0)
f(x)=0 that is not possible
f(0)=1

Take x=0 and y=10

f(10)+f(10)=2f(10)f(0)

f(10)+f(10)=2f(10)

f(10)=f(10)

f(10)f(10)=0

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