Question

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 $f(2012)?$

Answer 1

Given:

f(0) = 2

So first of all, we let x = 2012, y = 0:

Then, F(2012) = 2012 + f(0)

Since f(0) = 2, then f(2012) = 2012 + 2 = 2014.

To add, the process that relates an input to an output is called a function.

There are always three main parts of a function, namely:

Input

The Relationship

The Output

The classic way of writing a function is "f(x) = ... ".

What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.

What a function does with the input can be usually seen as:

f(x) = x2 reveals to us that function "f" takes "x" and squares it.