Question

Let f(x) = \sqrt{3 x - 5}

Use interval notation to indicate where f(x) is continuous.

Answer 1

f(x) is continuous over all values where 3x-5 is positive as you can only take the square root of a positive number to get a real answer. We get the equation 3x-5>0 which we can manipulate to 3x>5 and x>5/3 through the addition and multiplication properties of equality. To write this in interval notation we can observe the lowest point for x is 5/3 but it is strictly greater than 5/3 so the answers starts with (5/3 but there is no upward limit of the values of x so the second value for the interval is infinity so we get (5/3, infinity)

Answer 2

i keep putting that as my answer, and i get this as my response: (Hint: Functions like f(x) are continuous on the interval(s) on which they are defined. That is, they are continuous on their domains.)

Answer 3

Maybe try entering it as a decimal

Answer 4

decimals aren't allowed

Answer 5

hmmm. Oh I see try a bracket first so [5/3, infinity) because the squre root could also be equal to 0

Answer 6

you're right!! thank you so much.