Question

If you divide any natural number n by 4, you get a remainder r.

Answer 1

Given:

If you divide any natural number n by 4, you get a remainder r.

To find:

The values of r if $n=13;34;43;100$. Also find the domain and range.

Solution:

It is given that any natural number n by 4, you get a remainder r.

$\dfrac{n}{4}=q+\dfrac{r}{4}$

Where, n is a natural number, q is quotient, r is the remainder.

For $n=13$,

$\dfrac{13}{4}=3+\dfrac{1}{4}$

So, $r=1$.

For $n=34$,

$\dfrac{34}{4}=8+\dfrac{2}{4}$

So, $r=2$.

For $n=43$,

$\dfrac{43}{4}=10+\dfrac{3}{4}$

So, $r=3$.

For $n=100$,

$\dfrac{100}{4}=25+\dfrac{0}{4}$

So, $r=0$.

Therefore, the required value are $r=1,2,3,0$ if $n=13;34;43;100$ respectively.

The domain of the function is $\{13,34,43,100\}$ and the range of the function is $\{1,2,3,0\}$.