Question 1194424
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4. Is f(x) - g(x) = g(x) - f(x) true for all functions? Justify your answer.
**Writing one example will not justify your answer for ALL functions.
Which operation property can we use to prove this is true? **
(2 marks) 5. Is (f + g)(x) = (g + f )(x) true for all functions? Justify your answer.
**Writing one example will not justify your answer for ALL functions.
Which operation property can we use to prove this is true? **
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            Of two problems in the post,  I will consider and solve here 
            only one,  namely first one,  which goes under # 4.



<pre>
The question is "Is identity f(x) - g(x) = g(x) - f(x) true for all functions?".


The answer is "The identity f(x) - g(x) = g(x) - f(x) is not true for all functions."


    +--------------------------------------------------------------------------------+
    |    To prove that the answer is correct and disprove the original statement,    |
    |                                                                                |
    |            it is enough to present one single counter-example                  |
    |                  disproving the original statement.                            |
    +--------------------------------------------------------------------------------+


This disproving counter-example is  f(x) = 1, g(x) = 0,  two constant-value functions,

which produce self-contradictory identity  1 = -1  in real numbers.
</pre>


The problem is solved,
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the answer is given,
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and the original statement is disproved by presenting one contradicting example.



The instruction, &nbsp;written in the post between the signs &nbsp;(**) &nbsp;and &nbsp;(**), &nbsp;that follows the problem, 

is non-sensical gibberish, &nbsp;contradicting standard logic.



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As a post-solution notice and an advise for the future:


  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- never pack more than one problem per post.