In a function formula, can the independant variable $x$ ( ranging over $N$) be used as a simple figure inside a number? E.g. $ f(x)= 4,5x975$

Question

Suppose $x$ ranges over {0,1,2,3,4,5,6,7,8,9}.

Is $f(x) = 4,5x975$ a valid function formula ?

What about the case where $x$ ranges over the set of natural numbers.

In that case, $x$ would not represent necessarily the hundredth, 9 would not either necessarily represent the $10^{-3} $th, etc.

Which equivalent general formula would give us the value of $f(x)$ in case $x\gt9$? ( I mean, the case where $x$ has 2 digits or more?)

Mathsmerizing · Accepted Answer · 2020-03-12T09:22:08.560

0

yes as it can be expressed as f(x)= 450975+1000*x when x $\in$ {0,1,..9}

Over the set of natural number, we still can have the formula f(x)= $45*1000*10^{(⌊log10x⌋+1)}+975+1000*x$

Proof: How many digits does a number have? $\lfloor \log_{10} n \rfloor +1$

edited Mar 12 '20 at 09:22

answered Mar 12 '20 at 08:56

Mathsmerizing

2,003

Thanks for this link! – Mar 12 '20 at 09:16
@Ray LittleRock You are welcome – Mathsmerizing Mar 12 '20 at 09:19

score 0 · Answer 2 · answered Mar 12 '20 at 09:04

This is really just a notation question. If you're clear about what you mean with this notation ahead of time, then it's probably safe to use it as long as you're not using the standard notation side-by-side with this. This could cause confusion when the two notations collide, e.g. $10x$ is either a three-digit number with unknown ones digit or the product of $10$ and an unknown number.

In a function formula, can the independant variable $x$ ( ranging over $N$) be used as a simple figure inside a number? E.g. $ f(x)= 4,5x975$

2 Answers2