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

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

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

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