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

Domain is x∈(-∞;∞), since function is defined for all x.

Range is all values that function can have, x

^{4}is always positive or zero, therefore -x^{4}^{ }is always negative or zero, so -x^{4}+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]**