student34 said:Homework Statement
I constructed my own question to try to make sense of the following notation.
g(x) = 2√x g : X → Y. What does X and Y equal?
Homework Equations
For 2√x, x = or > than 0.
The Attempt at a Solution
g(x) = 2√x g : [0, ∞) → [0, ∞)
So X = Y = [0, ∞)
The reason why I am doing this is because my book shows this: g(x) = 2√x g : [1,∞) → [2,∞). Why does my book have a 1 instead of a 0 as an initial x value?
Dick said:You have found the LARGEST domain that that function can be defined on. X could always be defined to be a subset of that domain, in which case your job is to figure out the corresponding Y. Are you sure the book didn't tell you X=[1,∞)??
student34 said:The book just shows this, "g(x) = 2√x g : [1,∞) → [2,∞)" as an example of, "g : B → C". I just used X and Y for this thread.
Dick said:The book could also have said correctly that "g(x) = 2√x g : [4,∞) → [4,∞)". That would work also, right? Nothing in the problem really fixes what X HAS to be.
The domain of a function is the set of all possible input values (or independent variables) for the function. In other words, it is the set of values for which the function is defined.
The range of a function is the set of all possible output values (or dependent variables) that the function can produce. In other words, it is the set of values that the function can take on.
To determine the domain of a function, you need to identify any restrictions on the input values, such as a denominator cannot be equal to zero. The range of a function can be found by observing the graph of the function or by using algebraic methods to solve for the output values.
Yes, the domain and range of a function can be infinite, meaning there is no limit to the possible input and output values. This is often the case with exponential and logarithmic functions.
Understanding the domain and range of a function is important because it helps to determine the behavior and limitations of the function. It also allows us to identify any possible errors or restrictions in the function and to make accurate predictions about its output values.