Can someone explain to me why this fuction has the domain all real numbers?

Question

the function is...

f(x)=the third root of of X-4

why is the domain all real numbers?

(i didnt know how to put it on my computer)
(instead of taking the square root, there is a 3)

please help me out!
i dont understand

Answer 1

Because all real numbers can be substituted for x to get a real number f(x). If it were the square root (or any even-numbered root) instead of the cube root, the domain would be all real numbers greater than or equal to 4, since the square root of a negative number isn't real.

Answer 2

The domain is the set of replacement values for the independent variable, ie the x. Unless there are restrictions placed on the values of the variable in setting up the problem, the any number can be in the domain unless it leads to an undefined expression. The cube root isn't like the square root. That odd number gives you access to negatives. For example the cube root of -8 is -2. So any number can be used so the domain is all real numbers.

Answer 3

Because any real number can satisfy the function (they don't have to be rational numbers). Remember that the cube root of a negative number has to be a negative number. If the function were the square root of X-4, then for any X greater than 4, X-4 would be negative, and there would be no real number solution for the square root..

Answer 4

Because the third root can be applied both to positive and negative numbers: the square root of X is the number T that elevated to the third power will give X.

Immagine you have a negative number -T, then
(-T)^3 = (-1)^3 (T^3) = - (T^3) < 0

the situation is different with *square* roots (and all even roots), because the square of a number is always positive, but with third roots (and all odd roots) you don't have this problem.

Answer 5

domain is all real numbers because for any x you choose there is a cube root (called "cube", not "third"). On a computer you probably can raise to power 1/3. I'll check excel. excel does it.

on a pocket calculator only square roots are usually there.
for cube root, guess a number, multiply by itself 3 time and keep trying until you get the starting number.

Answer 6

It's domain is all real numbers because you can take the 3rd root of any real number and have a real and unique answer. To type it in, you could right it as (x-4)^(1/3).

Answer 7

The domain is the set of real numbers R for which the function is well defined. NOT well-defined is when, for instance, for the function does not exist for some values or the there is a division by zero. 1. e^anything is well-defined averywhere: dom(f) = all R 2. log is not defined for negative numbers and zero dom(f) must not include -3 and x < -3 dom (f) = all R x > -3 3. dom(f) = all R (same as #1) 4. ln is not defined for negative numbers and zero: t - 1will be zero when t = 1 and negative when t < 1 dom (f) = all R x > 1.

Answer 8

Its domain is all real numbers because its value is defined for all real values of X.  If it was something like
f(x) = x/(x-4)
it would be undefined at x=4.