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

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

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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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