When we compose functions, we must make sure that the output of the first function is part of the ___ of the second function.
domain
When we compose functions, we must make sure that the output of the first function is part of the domain of the second function. This is because the output of the first function serves as the input to the second function, and the input must be within the defined domain of the function in order for it to produce meaningful output.
For example, if we have two functions f(x) = 2x and g(x) = sqrt(x), and we want to compose them as (g o f)(x), we need to make sure that the output of f(x) = 2x is non-negative, as square root is only defined for non-negative real numbers. Thus, we must have x >= 0 for f(x), which tells us that the domain of f(x) is [0, infinity). Thus, the output of f(x) must be within this domain in order for (g o f)(x) to be meaningful.
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