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

[Md. Abde Mannaf]

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?

 

[Mentallic]

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?

 

[symbolipoint]

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).

 

[Md. Abde Mannaf]

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?

 

[JonnyG]

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)

 

[Mentallic]

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.