Domain math problem

Question

 What is the domain of the 6th root of t^4-9

Answer 1

f(t) = (t⁴-9)^1/6

 

f(t) is defined as long as t⁴-9 ≥ 0

 

t⁴-9 = (t²-3)(t²+3)

 

t⁴-9 = 0 when t = ±√3

 

When t ≤ -√3, t⁴-9 ≥ 0

When t is between -√3 and √3, t⁴ - 9 < 0

When t ≥ √3, t⁴-9 ≥ 0

 

Domain of f(t):  (-∞, -√3] ∪ [√3, ∞)

 

 

Answer 2

"Domain" is a term used in connection with a function. You present an expression.

 

t⁴ - 9 = 0 has only four roots:

(t² + 3)(t² - 3) = 0

{±√3, ±i√3}