3 + 2k
This is because multiplying by 1/5 is like dividing each term by 5
The answer to the problem is A
For this case, we have to:
By definition, we know:
The domain of ![f (x) = \sqrt [3] {x}](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%20%5Csqrt%20%5B3%5D%20%7Bx%7D)
is given by all real numbers.
Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root. Thus, it will always be defined.
So, we have:
![y = \sqrt [3] {x-2}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%20%5B3%5D%20%7Bx-2%7D)
with
: ![y = \sqrt [3] {- 2}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%20%5B3%5D%20%7B-%202%7D)
is defined.
![y = \sqrt [3] {x+2}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%20%5B3%5D%20%7Bx%2B2%7D)
with ![x = 0:\ y = \sqrt [3] {2}](https://tex.z-dn.net/?f=x%20%3D%200%3A%5C%20y%20%3D%20%5Csqrt%20%5B3%5D%20%7B2%7D)
is also defined.
has a domain from 0 to ∞.
Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.
Thus, we observe that:
is not defined, the term inside the root is negative when.
While 
if it is defined for .
Answer:
Option b
The correct order would be:
5/64 x 3, 1/16 x 3, 3/32 x 4, 11/64 x 4, 7/16 x 3, 3/4 x 2, 3/8 x 4, 1 7/8 x 4, 2.25 x 2, 1.5 x 4, 3 3/8 x 3, 3.75 x 3
First we have to take all of the numbers and do the multiplication. It's often easiest to turn them in to decimals so that you have a common form.
3/32 x 4 = 3/8 = .375
3/4 x 2 = 3/2 = 1.5
1 7/8 x 4 = 15/4 = 3.75
2.25 x 2 = 4.5
1.5 x 4 = 6
3/8 x 4 = 3/2 = 1.5
5/64 x 3 = 5/32 = .156
3.75 x 3 = 11.25
1/16 x 3 = 3/16 = .1875
7/16 x 3 = 21/16 = 1.31
3 3/8 x 3 = 81/8 = 10.125
11/64 x 4 = 11/16 = .687
Now we can use those to put in order.
5/64 x 3 = 5/32 = .156
1/16 x 3 = 3/16 = .1875
3/32 x 4 = 3/8 = .375
11/64 x 4 = 11/16 = .687
7/16 x 3 = 21/16 = 1.31
3/4 x 2 = 3/2 = 1.5
3/8 x 4 = 3/2 = 1.5
1 7/8 x 4 = 15/4 = 3.75
2.25 x 2 = 4.5
1.5 x 4 = 6
3 3/8 x 3 = 81/8 = 10.125
3.75 x 3 = 11.25
Which if you are looking for without the extra terms, you can check the answer at the top.
It’s B I hope this helps :)
