Question

following function is what kind if function f:Z to Z defined by f(x) =x^2+x​

Answer 1

Answer:

Let x,y∈Z such that f(x)=f(y)

⇒x

2

+x=y

2

+y

⇒x

2

−y

2

+x−y=0

⇒(x−y)(x+y+1)=0

⇒x=y or x=−y−1

Since f(x)=f(y) does not yield the unique solution x=y but also provides the solution x=−y−1,

So it is not a one - one function.

For example, if y=1, then x=1 from x=y and also x=−2 from y=−x−1

This means that 1 and −2 have the same image

Hence, f is a many-one function