.
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.
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.
The problem is solved,
the answer is given,
and the original statement is disproved by presenting one contradicting example.
The instruction, written in the post between the signs (**) and (**), that follows the problem,
is non-sensical gibberish, contradicting standard logic.
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As a post-solution notice and an advise for the future:
- never pack more than one problem per post.