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Hurkyl

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Can you find the domain of f or g individually?

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HallsofIvy

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Then, however, f(x) must be such that g(f(x)) is defined. Start with the domain of f and delete those values for which g(f(x)) is

In your original example, the domains of both g and f are 'all real numbers' so the domain of g(f) is also 'all real numbers'.

If you had g(x)= sqrt(x), f(x)= 3x- 1, the domain of f is all real numbers but the domain of g is only non-negative numbers. For what x is 3x-1>= 0?

Conversely, if g(x)= 3x-1, f(x)= sqrt(x), The domain of f is non-negative numbers. Since g(x) is defined for all x, g(f(x)) is defined for all numbers for which f is defined: non-negative numbers.

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