Question

Show that gof is not one one ( pls be careful I need gof not fog)​

Answer 1

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

FORMULA TO BE IMPLEMENTED

A function $f : A \mapsto \: B$ is said to be one - one if

$x_1 \ne x_2 \: \: \implies \: \:f( x_1) \ne \: f( x_2 \: )$

CALCULATION

Here it is given that

$f \: = \{ (2,5),(4,9),(6,3),(8,7) \: \}$

$g \: = \{ \: (3,49), (5,81), (7,9), (9,81) \: \}$

So

$(gof)(2) = g(f(2)) = g(5) = 81$

$(gof)(4) = g(f(4)) = g(9) = 81$

$(gof)(6) = g(f(6)) = g(3) = 49$

$(gof)(8) = g(f(8)) = g(7) = 9$

So

$(gof) = \{ (2,81),(4,81),(6,49),(8,9) \: \}$

Clearly

$2 \ne \: 4 \: \: but \: \: (gof)(2) =(gof)(4) = 81$

So $(gof)$maps two different point 2 & 4 to the same point 81

Hence$(gof)$is not one - one

Answer 2

Answer:

IT HAS TWO DIFFERENT POINTS 2 AND 4 THAT IS 81.

Step-by-step explanation:

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