Question

What is the inverse of the function F= {(-2, -3), (-2, -1), (-4, -1), (5, 0)}?

Answer 1

Answer:

The function F has no inverse.

Step-by-step explanation:

Given that the function is

$F=\{(-2,-3),(-2,-1),(-4,-1),(5,0)\}$

This means that function maps -2 to -3, -2 to -1, -4 to -1 and 5 to 0.

When we find the inverse we take each number in the range which are {-3,-1,0} and find its preimage under this function F. But the number -1 is an image of two numbers -2 and -4. So the function is not one-one and hence F has no inverse.

An inverse exist if and only if the function is both one-one and onto.

Answer 2

SOLUTION

TO DETERMINE

The inverse of the function

F = {(-2, -3), (-2, -1), (-4, -1), (5, 0)}

CONCEPT TO BE IMPLEMENTED

INJECTIVE FUNCTION :

$\sf{A \: function \: f : A \to B \: is \: said \: to \: be \: injective \: if}$

$\sf{For \: \: x_1 \ne x_2 \: \: we \: have \: \: f(x_1) \ne f(x_2)}$

SURJECTIVE FUNCTION :

$\sf{A \: function \: f : A \to B \: is \: said \: to \: be \: surjective}$

if for every element y in the co-domain B there exists a pre-image x in domain set A such that y = f(x)

BIJECTIVE FUNCTION :

$\sf{A \: function \: f : A \to B \: is \: said \: to \: be \: bijective}$

if f is both injective and surjective

EVALUATION

Here the given function is

F = {(-2, -3), (-2, -1), (-4, -1), (5, 0)}

Now a function F is said to have inverse if F is bijective

We see that F maps - 2 of its domain to two different elements - 3 & - 1

So F is not injective

Thus F is not bijective

Hence the inverse of the function F does not exist

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