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

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In summary, the difference between abs(1/x^2) and 1/x^2 is that the absolute value function always returns a positive value, while the latter can also return negative values. However, when graphed, both functions result in the same graph. This means that the functions are equal for all real numbers, but not for imaginary numbers.
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Md. Abde Mannaf
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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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  • #2
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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  • #3
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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  • #4
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?
 
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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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  • #6
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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Related to What is difference between abs(1/x^2) and 1/x^2 ?

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

The difference between abs(1/x^2) and 1/x^2 is that abs(1/x^2) represents the absolute value of 1/x^2, which means that it always returns a positive value. On the other hand, 1/x^2 represents the inverse of x^2, which means that the value can be either positive or negative depending on the value of x.

2. How do the graphs of abs(1/x^2) and 1/x^2 differ?

The graph of abs(1/x^2) is a V-shaped curve that intersects the x-axis at (0,0) and approaches the y-axis but never touches it. On the other hand, the graph of 1/x^2 is a hyperbola that approaches both the x-axis and y-axis but never touches either of them.

3. Can the value of abs(1/x^2) ever be negative?

No, the absolute value function always returns a positive value, so the value of abs(1/x^2) can never be negative.

4. How does the value of abs(1/x^2) change as x approaches 0?

As x approaches 0, the value of abs(1/x^2) increases infinitely. This is because as x gets closer to 0, the value of 1/x^2 also gets closer to infinity, and the absolute value function always returns a positive value.

5. What is the importance of the absolute value function in mathematics?

The absolute value function is important in mathematics because it allows us to always have a positive value, regardless of the input. This is useful when dealing with equations or graphs that involve negative numbers, as it helps simplify the problem and make it easier to understand and solve.

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