Question

If R is the set of all real numbers then, check whether the function

defined by ( ) is one to one function or not?​

Answer 1

SOLUTION

TO CHECK

If $\sf{ \mathbb{R}}$ is the set of all real numbers then, check whether the function defined by

$\sf{f(x) = |x| }$

is one to one function or not

CONCEPT TO BE IMPLEMENTED

A real valued function f is said to be one to one if

$\sf{for \: \: x_1, x_2 \in \mathbb{R} }$

$\sf{f(x_1) = f( x_2) \: \: implies \: \:x_1 = x_2 }$

EVALUATION

Here $\sf{ \mathbb{R}}$ is the set of all real numbers

The function is defined by

$\sf{f(x) = |x| }$

$\sf{Now \: we \: take \: \: - 1,1 \in \mathbb{R}}$

Such that

$\sf{f( - 1) = | - 1| = 1}$

$\sf{f(1) = |1| = 1 }$

$\sf{Thus \: \: - 1 \ne 1 \: \: but \: \: f( - 1) = f(1)}$

So f is not one to one function

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