MarkFL said:I would use the definition:
\(\displaystyle |x|\equiv\begin{cases}-x & x<0\\ x & 0\le x \\ \end{cases}\)
So, what you want to find, is where the function \(\displaystyle f(x)=x^2-1\) is negative, and where is it non-negative.
MarkFL said:The second one is correct...do you see why the first is not?
The function $f(x)=x^2-1$ is negative on $(-1,1)$, otherwise is is non-negative, so another way we could define $|f(x)|$ is:
\(\displaystyle |f(x)|=\begin{cases}1-x^2 & |x|<1 \\ x^2-1 & 1\le|x| \\ \end{cases}\)
MarkFL said:You left out $1\le x$. Also, we really don't see special cases for when the expression is equal to zero, we just need to differentiate between negative and non-negative.
The function of a scientific experiment is to test a hypothesis or to gather data that can be used to support or refute a scientific theory. It allows scientists to make observations, collect data, and draw conclusions based on evidence.
The purpose of defining a function in scientific research is to clearly define the role or purpose of a particular process or mechanism within an experiment. This allows for better understanding and interpretation of the results.
A function is defined in a scientific experiment by describing its specific role or purpose within the experiment and how it relates to the overall goal or hypothesis being tested. This can include the variables involved, the methods used, and the expected outcome.
Defining a function in a scientific experiment is important because it helps to ensure that the experiment is well-designed and that the results are accurate and reliable. It also allows for better communication and replication of the experiment by other scientists.
Yes, a function can change in a scientific experiment if new evidence or data suggests that the original function was incorrect or incomplete. This is a normal part of the scientific process and allows for the development and refinement of scientific knowledge.