Question
Show that the function $f: N \rightarrow N$ defined by $f(m)=m^2+m+3$ is one-one function
✓
Answer
$N=\{1,2,3,4,5, \ldots .$}
$f(m)=m^2+m+3$
$f(1)=1^2+1+3=5$
$f(2)=2^2+2+3=9$
$f(3)=3^2+3+3=15$
$f(4)=4^2+4+3=23$
$f=\{(1,5)(2,9)(3,15)(4,23)\}$
From the diagram we can understand different elements in (N) in the domain, there are different images in (N) co-domain.
∴ The function is a one-one function.
$f(m)=m^2+m+3$
$f(1)=1^2+1+3=5$
$f(2)=2^2+2+3=9$
$f(3)=3^2+3+3=15$
$f(4)=4^2+4+3=23$
$f=\{(1,5)(2,9)(3,15)(4,23)\}$
From the diagram we can understand different elements in (N) in the domain, there are different images in (N) co-domain.
∴ The function is a one-one function.
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