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interval notation

give the range and the domain in interval notation of f(x) = -x^4+3

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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Domain is x∈(-∞;∞), since function is defined for all x.
 
Range is all values that function can have, x4 is always positive or zero, therefore -x4 is always negative or zero, so -x4+3 is less than or equal to 3, f(x)≤3 for all x.
 
Therefore, range is f(x)∈(-∞;3].
 
Answer:
 
D: x∈(-∞;∞)
R: f(x)∈(-∞;3]