Finding the Domain of a Composite Function
For a composite function y = f(g(x)), its domain is the set of all x such that the range of g(x) is contained within the domain of f(u). Applicable Conditions:…
Syllabus path: Functions › Concepts and Properties of Functions › Domain of a Function
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CSCA Mathematics Formula Reference
Formula and explanation
For a composite function y = f(g(x)), its domain is the set of all x such that the range of g(x) is contained within the domain of f(u). Applicable Conditions: Functions f and g are composable. Brief Explanation: First find the range of the inner function g(x), then ensure this range is a subset of the domain of the outer function f(u), and finally solve for the range of x.
Related tutorial and examples
Domain of a Function
Domain of a Function 1. Concept The domain of a function is the set of all possible values for the independent variable x. It is one of the three essential elements of a function. Simply put, the domain consists of all real numbers x for which the function y = f(x) is defined (ma…
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