0

I am confused as to what really a function is ?

  1. Is a function the steps by which we get the output from an input ?
  2. Or is it the name of the process by which we get the output from an input ?
Ashok Sharma
  • 31
  • 4

2 Answers2

0

Consider the function $x\mapsto x^2$. That describes the steps from input to output. Now you may refer to that function by a name, say $f$, so you write $f\colon x\mapsto x^2$

Michael Hoppe
  • 18,103
  • 3
  • 32
  • 49
  • Why the downvote? Did I misunderstand the question? – Michael Hoppe Mar 20 '19 at 12:56
  • I downvoted your reply for two reasons. Firstly, because it did not address the real question, i.e., what is a function. Secondly, because your decision not to involve the domain and the codomain in the discussion, will in my opinion, push the OP in the wrong direction. I think that very basic questions should be answered at length. – Carl Christian Mar 20 '19 at 21:24
0

Simply put, a function is basically the description or the rule of the dependence of the output on the input. It may also be seen as a mapping of the set $X$ - the domain to the set $Y$- the codomain. Notation-aly $f: X\mapsto Y$.

Take the example of $f(x)=x^2$. Let $X$ be the set of Real Numbers denoted $\mathbb{R}$. Clearly you can observe from the graph of $y=x^2$ that $f$ maps the input that is the real line to the positive real plane including $y=0$. Again, Notation-aly $f(x)=x^2 \mid f:\mathbb{R}\mapsto \mathbb{R^+}\cup \{0\}$.

I would suggest you consult Wikipedia's page on Functions for deeper detail.

Paras Khosla
  • 6,481
  • 1
    You didn't make precise what you mean with "the description or the rule". Note that two functions can be equal, but have different "descriptions". Furthermore, not every function needs to have a "concrete" rule. Just imagine the choice-function provided by the axiom of choice. Typically, there is no "description or rule" for the function. – Babelfish Mar 20 '19 at 10:20