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vfiekz [6]
3 years ago
7

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 $f(2012)?$

Mathematics
1 answer:
marusya05 [52]3 years ago
3 0

<span>Given:

f(0) = 2</span>

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

<span>
Then, F(2012) = 2012 + f(0)

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

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

 

 

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

</span>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:

 

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

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Answer:

see explanation

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

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here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence

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n² + 4n - 165 = 0 ← in standard form

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equate each factor to zero and solve for n

n + 15 = 0 ⇒ n = - 15

n - 11 = 0 ⇒ n = 11

but n > 0 ⇒ n = 11



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