Given:
If you divide any natural number n by 4, you get a remainder r.
To find:
The values of r if [tex]n=13;34;43;100[/tex]. Also find the domain and range.
Solution:
It is given that any natural number n by 4, you get a remainder r.
[tex]\dfrac{n}{4}=q+\dfrac{r}{4}[/tex]
Where, n is a natural number, q is quotient, r is the remainder.
For [tex]n=13[/tex],
[tex]\dfrac{13}{4}=3+\dfrac{1}{4}[/tex]
So, [tex]r=1[/tex].
For [tex]n=34[/tex],
[tex]\dfrac{34}{4}=8+\dfrac{2}{4}[/tex]
So, [tex]r=2[/tex].
For [tex]n=43[/tex],
[tex]\dfrac{43}{4}=10+\dfrac{3}{4}[/tex]
So, [tex]r=3[/tex].
For [tex]n=100[/tex],
[tex]\dfrac{100}{4}=25+\dfrac{0}{4}[/tex]
So, [tex]r=0[/tex].
Therefore, the required value are [tex]r=1,2,3,0[/tex] if [tex]n=13;34;43;100[/tex] respectively.
The domain of the function is [tex]\{13,34,43,100\}[/tex] and the range of the function is [tex]\{1,2,3,0\}[/tex].
