The discussion focuses on understanding the input and output methods for determining the domain and range of composite functions, specifically in the context of functions like f(g(x)). Key points include that the domain of the composite function f(g(x)) is defined by the range of g(x), which must be a subset of the domain of f(x). Additionally, the range of the composite function can be determined by analyzing the output values of f when g(x) is applied. Examples provided include f(x) = sqrt(x-2) and g(x) = x+3, illustrating how to find the range of their sum.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone seeking to deepen their understanding of composite functions and their properties.
"Textspeak" isn't allowed here. Please don't write "u" for "you".Coco12 said:U plug in x into the equation to find out what numbers y is greater than or equal to and same for the 3
So you plug in x values into equation to get the range? Does this always work. Because I know in some cases the domain is all real numbers but the range might not be.scurty said:Okay, that makes sense now. You plug the x values into the equation, not the range.
Coco12 said:So you plug in x values into equation to get the range? Does this always work. Because I know in some cases the domain is all real numbers but the range might not be.