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if f(x+y)=f(xy),ybelongs to R,then prove that f is a constant function?

if f(x+y)=f(xy),ybelongs to R,then prove that f is a constant function?

Grade:12

3 Answers

Saravan V
34 Points
9 years ago

Let x be any real, and y=0.
Then f(x+0) = f(x*0)

=> f(x) = f(0) for all real x.
Hence the function is a constant function. 

FITJEE
43 Points
9 years ago

Let x be any real, and y=0.
Then f(x+0) = f(x*0)

=> f(x) = f(0) for all real x.
Hence the function is a constant function. BECAUSE IT IS A PROPERTY OF CONSTANT FUNCTION.


 

yashwanth
13 Points
4 years ago
LET US TAKE Y=0 , SUBSTITUTE Y value in f(x+y)
then f(x+0)=f(x*0)
here for any real number of x,y we get f(x+y)=f(xy)= constant

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