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Jeff12341234
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I used the linear equation method to solve a D.E. and got y=3/4 at the end. I'm asked to find the interval of definition but I don't know how to do that when Y is just a constant :/
Jeff12341234 said:So the interval of definition would be (-∞,∞)?
I just don't get how a function can have a domain when it's just a constant...
Every function has a domain.Jeff12341234 said:So the interval of definition would be (-∞,∞)?
I just don't get how a function can have a domain when it's just a constant...
I wouldn't use the word "range" when you're talking about the domain, because of confusing the issue with the function's range.Mute said:If your function is y(t) = 3/4, it means that for any t you give the function as an input, the function returns the value 3/4. So, the domain is whatever range of values of t you are allowed to put into your function. It doesn't matter that your function happens to return a constant in this case.
An interval of definition is the set of all values of the independent variable for which the given function is defined. In other words, it is the range of values that can be input into the function to produce a valid output.
Knowing the interval of definition is important because it helps us understand the limitations and restrictions of a given function. It also allows us to identify any potential discontinuities or undefined points within the function.
To determine the interval of definition, you must first identify any values that would result in an undefined output. These values may include division by zero, taking the square root of a negative number, or any other operations that are not defined for certain values. The interval of definition will then be the set of all valid input values that do not result in undefined outputs.
Yes, the interval of definition can change for a given function. This can happen when the function is modified or when a new restriction or limitation is introduced. It is important to always check for changes in the interval of definition when working with functions.
When y equals a constant, the interval of definition will depend on the specific value of the constant. If the constant is a real number, then the interval of definition will be all real numbers. However, if the constant is a complex number, then the interval of definition may be restricted to certain values depending on the function.