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..​

Answer 1

Answer:

f:Z➡️Z

f(x)=x²+x

x€Z

so x belongs to z is many one

Answer 2

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

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