What is difference between abs(1/x^2) and 1/x^2 ?

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The discussion centers on the mathematical difference between abs(1/x^2) and 1/x^2, with participants noting that both expressions yield the same graph for real numbers. However, the absolute value function alters the output for complex numbers, specifically when x is imaginary. While the graphs appear identical, the functions are not equivalent due to the behavior of absolute values in different domains. The conversation emphasizes that the absolute value ensures non-negativity, affecting the function's outputs. Ultimately, the conclusion is that while the graphs are the same, the functions are not equal in all contexts.
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what is difference between abs(1/x^2) and 1/x^2 .
i am using https://graphsketch.com/ graph result is same. what do you think?
 
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Md. Abde Mannaf said:
what is difference between abs(1/x^2) and 1/x^2 .
i am using https://graphsketch.com/ graph result is same. what do you think?

Well, what do you think? What does the absolute value do?
 
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Md. Abde Mannaf said:
what is difference between abs(1/x^2) and 1/x^2 .
i am using https://graphsketch.com/ graph result is same. what do you think?
They are both equal. That is, if you allow for only real numbers.

Think what happens for x=i.
abs(1/(i^2)) versus 1/(i^2).
 
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Mentallic said:
Well, what do you think? What does the absolute value do?
i think it is same. function is not same but graph is same. that is my question is are equal?
 
If the graphs are the same, then the functions must be the same. The graph of a function f is the set of all points (x, f(x)). The graph of a function g is the set of all points (x, g(x)). If (x, f(x)) = (x, g(x)) then it is easy to see that you must have f(x) = g(x)
 
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Md. Abde Mannaf said:
i think it is same. function is not same but graph is same. that is my question is are equal?

You can figure it out through some simple reasoning. What does the absolute value do? Give me some examples. And then, what values can't 1/x2 ever be? For example, ##x^2\geq 0## for all values of x, so x2 can't ever be negative.
 
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