Show that the function f: Z → Z defined by f (x) = x^2 + x for all x belongs to Z is a many-one function. Solve this f

Question

Show that the function f: Z → Z defined by f (x) = x^2 + x for all x belongs to Z is a many-one
function.

Solve this for brainliest answer..​

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Kaylee 1 month 2021-08-19T22:29:43+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-19T22:30:57+00:00

    Answer:

    f:Z➡️Z

    f(x)=x²+x

    x€Z

    so x belongs to z is many one

    0
    2021-08-19T22:31:08+00:00

    \displaystyle\huge\red{\underline{\underline{Solution}}}

    A function

    f \: :A  \mapsto \: B

    is said to be many one function if for

    x_1 \ne \: x_2 \:  \: we \:have \: f(x_1) = f( x_2)

    TO PROVE

    The function

    f : \mathbb{ Z } →\mathbb{ Z } \:  \: defined \: by \:  \: f(x) =  {x}^{2}  + x \:   \:  \: \forall \: x \in \mathbb{ Z }

    is a many-one function.

    PROOF

    Here we take two points

    0 \: , - 1 \in \: \mathbb{ Z } \:  \: with \:  \: 0 \ne \:  - 1

    So

    f(0) =  {0}^{2}  + 0 = 0

    f( - 1) =  {( - 1)}^{2}  - 1 = 1 - 1 = 0

    Thus for

    0 \: , - 1 \in \: \mathbb{ Z } \:  \: with \:  \: 0 \ne \:  - 1 \:  \: but \: f(0) = f(  - 1)

    RESULT

    Hence f is a many-one function

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