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)? Thank you!
To find the value of f(2012), we can substitute values into the given functional equation and simplify.
First, let's substitute x = 2012 and y = 0 into the equation:
f(2012 + 0) = 2012 + f(0)
Simplifying the left side of the equation:
f(2012) = 2012 + f(0)
Since we are given that f(0) = 2, we can substitute this value into the equation:
f(2012) = 2012 + 2
Simplifying further:
f(2012) = 2014
Therefore, f(2012) = 2014.