Definition of the Composition of Two Functions

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To define the composite function g(f(x)): A -> C meaningfully, the range of f must be a subset of the domain of g. This ensures that for every output of f, there is a corresponding input for g. The condition can be expressed as f(A) ⊆ B, where f(A) is the image of f over its domain A. Understanding the image of a function is crucial for establishing this relationship. A clear grasp of these concepts is essential for solving the problem effectively.
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Homework Statement



In general, let f: A -> T and g: B -> C. Find a condition on the domain of g (other than B = T) that results in a meaningful definition of the composite function g((f(x)): A -> C.


Homework Equations



None.


The Attempt at a Solution



I could not find a starting place for this problem.
 
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You might want to recall the definition of the image of a function.
 

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