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Is x squared a Monotonic Function?

Updated: 4/28/2022
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14y ago

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No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.

No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.

No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.

No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.

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No. For x < 0, it decreases, for x > 0, it increases. In each of these two parts, it is monotic, though.

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Why is x squared a inverse function?

X squared is not an inverse function; it is a quadratic function.


Is a monotonic function a bijection?

No. For example, y = 7 is monotonic. It may be a degenerate case, but that does not disallow it. It is not a bijection unless the domain and range are sets with cardinality 1. Even a function that is strictly monotonic need not be a bijection. For example, y = sqrt(x) is strictly monotonic [increasing] for all non-negative x. But it is not a bijection from the set of real numbers to the set of real numbers because it is not defined for negative x.


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They can be either, but not together. y = x and y = -x are both monotonic.


Why does a square root have two answer?

Answer: As for example the square root of 16 is -4 or +4 because -4 times -4 = 16 and 4 times 4 = 16 Answer: There are two "answers", because there are two numbers which, when squared, give you a specified number. The reason for this is that the square function is not monotonic - this results in complications when determining the inverse function. For more details, read about "monotonic function", for example in the Wikipedia.


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Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).


What is the inverse function of xx?

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