Question

determine the domain of this function. cube root of 3t+12
show in interval notation.

Answer 1

\[\sqrt[3]{3t+12}\]

Answer 2

Domain should be all real numbers because you're taking an odd root. You can take odd roots of negative numbers without getting imaginary/complex numbers

Answer 3

ok

Answer 4

There is no restriction caused by the cube root (we can use positive, zero, and negative values and still have a real (although probably not rational) output). So, we can use all real numbers

( - infinity, infinity )

Answer 5

because of the cubed root correct

Answer 6

Yep -- essentially, if you have an odd index / root, you have no restrictions for input.

Answer 7

ok I will write that in my notes thanks a million