Pere Callahan said:Is your question to find all functions [itex]f:\mathbb{R}\times \mathbb{R}\to\mathbb{R}[/itex] such that [itex]f(x)+f(y^2)=f(x^2+y)\quad\forall x,y \in \mathbb{R}[/itex]?
If you want us to help you, show some effort. What have you tried so far?
Pere Callahan said:Is the function defined on R or on RxR...?
Take some special values for x and y, like x=0, or y=0 or x=y and see where it takes you.
Pere Callahan said:Sorry, I do not understand what you are saying. I suggest you try and find someone to help you who speaks your language.
"All of the functions that achieve defined" refer to a set of mathematical functions that take in an input and produce an output that is defined or has a specific value. These functions are also known as "well-defined" functions.
Scientists determine if a function is well-defined by checking if it produces a unique output for every input and if the output is within the specified range of values. If the function meets these criteria, it is considered well-defined.
It is important for functions to be well-defined because it ensures that the function is consistent and reliable. This is crucial for scientists as they use these functions to make predictions and draw conclusions in their research.
If a function is not well-defined, it can lead to incorrect results and unreliable conclusions. It can also cause confusion and inconsistencies in scientific findings. Therefore, it is important for scientists to carefully define and verify their functions before using them in their research.
No, not all functions can achieve defined. For a function to be well-defined, it must follow certain rules and criteria. If a function does not meet these criteria, it cannot be considered well-defined and may not achieve a defined output for every input. This is why it is important for scientists to carefully select and define their functions for their research.