# What are the additive and multiplicative identities in the ring of all functions $f: \mathbb{R}\to\mathbb{R}$ [closed]

What are the additive and multiplicative identities in the ring $f: \mathbb{R}\to\mathbb{R}$ under the operations: $(f+g)(x) = f(x)+g(x)$ and $(fg)(x) = f(x)g(x)$

I know that the additive identity implies the first function $(f(x)+g(x))$ where applying the function does nothing to it i.e. $x=0$

## closed as unclear what you're asking by Stefan Mesken, Paolo Leonetti, Dietrich Burde, Shaun, user223391 Oct 3 '17 at 22:04

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• You really need to write up explicitly what you have been asked to prove. That might also help you clear up the confusion about what this ring is. – Tobias Kildetoft Oct 3 '17 at 18:01
• $f(x)+ 0(x) = f(x)$. – Robert Israel Oct 3 '17 at 18:03

The additive identity is $\mathbf{0}$ such that $\mathbf{0}(x)=0$ for all $x$.
The multiplicative identity is $\mathbf{1}$ such that $\mathbf{1}(x)=1$ for all $x$.