Question

The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of (u circle v) (x)?

u(x) Not-equals 0 and v(x) Not-equals 2
x Not-equals 0 and x cannot be any value for which u(x) Equals 2
x Not-equals 2 and x cannot be any value for which v(x) Equals 0
u(x) Not-equals 2 and v(x) Not-equals 0

Answer 1

c

Explanation:

edge 2020

Answer 2

The domain would include all the real values except
`x = 2` and the x for which
`v(x) = 0`.

Hence, the restrictions would be:

• 
  `x\:\\e \:2`

and

• 
  `v\left(x\right)\:\\e \:0`

Explanation:

Given

The domain of u(x) is the set of all real values except 0.

so

domain = (-∞, 0) U (0, ∞)

The domain of v(x) is the set of all real values except 2.

so

domain = (-∞, 2) U (2, ∞)

For the function composed function (u circle v) (x), we need to apply first the function
`v(x)` whose argument is (x), and then the function
`u (v(x) )` whose argument is
`v(x)`.

Please note that the domain of the composed function (u circle v) (x) must have to take into account the values for which both functions u(x) and v(x) are defined.

Therefore, the domain would include all the real values except
`x = 2` and the x for which
`v(x) = 0`.

Hence, the restrictions would be:

• 
  `x\:\\e \:2`

and

• 
  `v\left(x\right)\:\\e \:0`