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Let f be a function such that f(x+y)=x+f(y) for any two real numbers x and y. If f(0)=2, then what is f(2012)?

Guest Jul 17, 2018

Best Answer 

 #1
avatar+27057 
+1

Let x = -2012 and y = 2012. Then:

 

f(-2012 + 2012) = -2012 + f(2012)

 

f(0) = -2012 + f(2012)

 

2 = -2012 + f(2012)

 

f(2012) = 2014

Alan  Jul 17, 2018
 #1
avatar+27057 
+1
Best Answer

Let x = -2012 and y = 2012. Then:

 

f(-2012 + 2012) = -2012 + f(2012)

 

f(0) = -2012 + f(2012)

 

2 = -2012 + f(2012)

 

f(2012) = 2014

Alan  Jul 17, 2018

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