webwork question

(1 pt) 


How do I format an answer for this problem?
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Find the domain of the vector functions, r(t), listed below.
You may use "-INF" for −∞ and use "INF" for ∞ as necessary, and use "U" for a union symbol if a union of intervals is needed.
a) r(t)=⟨ln(7t),t+18‾‾‾‾‾‾√,118−t√⟩


b) r(t)=⟨t−8‾‾‾‾‾√,sin(3t),t2⟩



c) r(t)=⟨ e−8t,tt2−9√,t1/3⟩
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  AnSwEr0001: (-inf,inf)U(-inf,inf)U[0,inf)
        AnSwEr0002: (-inf,inf)
        AnSwEr0003:
Number of correct attempts:   0
Number of incorrect attempts: 18
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Your formatting is fine.  What seems to be missing here seems to be a basic lack of knowledge about the domains of some basic functions and/or maybe a lack of understanding what "the domain of a function" means.  In all cases the domain of a vector function is at most the intersection of the natural domains of the component functions.  The domain of a real valued function f(x) is the set of all values x for which f(x) is defined as a (finite!) real number.  Given a graph of the function in the xy-plane, it will be the values on the x-axis over which a vertical line intersects the graph of the function.  See this wiki page for the graph of the log function, this one for the graph of the square root.  For an example, the domain of ln(x) is (0, INF), the domain of √x is [0,INF), the domain of 1/√x  is (-INF, 18]; together the domain of r(t)=<ln(9-t),√t, 1/√(3+t)> will be the intersection of the intervals (-INF,9), [0,INF), (-3,INF), which gives [0,9).