Please help me, this is HW that I have been trying to solve but I can't.

Question

Please solve this question.

I really need an explanation down to the answers because I have been having sooo much trouble solving it.

Describe the interval(s) on which the function is continuous. (enter your answer in interval notation.)

f(x)= X+5/ sq root X

Answer 1

First, we notice that f(x) = x + 5 / √(x), is only defined for x >= 0, since the square root of any negative number is not defined in the real numbers. Second, since that square root is in the denominator and √(0) = 0, then f(x) as x goes to 0 is not defined either, so f(x) is continuous on the interval (0, ∞), where the parentheses denote that x cannot = 0 nor = ∞.