# Math Help - About functions

1. ## About functions

Hi. PLease can you say me:
Can i to represent a function as:

Is this function injective and constant both? Why? Thank you

2. ## Re: About functions

I'm not sure I understand your question. Are you saying that f is a function from A to B, that A contains the single member "u", B contains the single member "8" (or possibly "g"?) and f(u)= 8? If so, it is both "injective" and "surjective". It cannot be a "constant" function since f(u) is not u.

3. ## Re: About functions

Originally Posted by HallsofIvy
I'm not sure I understand your question. Are you saying that f is a function from A to B, that A contains the single member "u", B contains the single member "8" (or possibly "g"?) and f(u)= 8? If so, it is both "injective" and "surjective". It cannot be a "constant" function since f(u) is not u.
The function $f:\mathbb{R} \to \mathbb{R}$ defined by $f(x) = 0$ is a constant function, and $f(x) \neq x$. A constant function means that the output is constant over the entire domain. So, yes, the OP's function (if it only acts on a single point) is a constant function.

4. ## Re: About functions

Ah, yes, don't know why I said that. Thanks for catching that!