Question

f(t)=square root of t + 7th root of t. I'm supposed to find the domain. Don't know where to begin.

Answer 1

the domain of a function is all the values of t where f(t) is not equal to zero.

Answer 2

Sorry I meant where f(t) is not undefined.

Answer 3

so, (-inf., 0) u (0, inf) ?

Answer 4

square root of a number is undefined if the the number is a negative number. Am I right?

Answer 5

right. so no negatives. therefore domain must be from 0 to some number. Am i on the right track?

Answer 6

greater than 0, I mean.

Answer 7

7th root of t can also be written as t^(1/7), right?

Answer 8

Those are both correct. The domain of a 7th root includes negatives, but the domain of a 2nd root does not, so there's a restriction. Your domain is greater than or equal to 0. Yes 7th root of t = t^(1/7)

Answer 9

so in interval notation, I would write: (0,infinity)?

Answer 10

You will include 0.

Answer 11

so [0,infinity)

Answer 12

You got it.