Question

Suppose that the functions u and w are defined as follows.

U(x) = x² +3
w (x) = sqrt of x+2
Find the following
(u • w)(2)=
(w • u) (2)=

Answer 1

Answer(there are assumptions for this answer that you need to confirm and look at):

Assumptions:
`u(x)=x^2+3` and
`w(x)=√(x+2)`

Answer if the operation is multiplication:

If you meant a closed dot which is the symbol for multiplication.

`(u \cdot w)(2)=14`

`(w \cdot u)(2)=14`

Answer if the operation is composition:

If you meant an open dot which is the symbol for composition.

`(u \circ w)(2)=7`

`(w \circ u)(2)=3`

Note: I don't know if you actually meant
`w(x)=√(x+2)` or if
`w(x)=√(x)+2`. Please let me know one way or the other.

Explanation:

If we assume the functions are:

`u(x)=x^2+3`

`w(x)=√(x+2)`

`u \cdot w=w \cdot u` since multiplication is commutative.

`u(2)=2^2+3`

`u(2)=4+3`

`u(2)=7`

`w(2)=√(2+2)`

`w(2)=√(4)`

`w(2)=2`

We are asked to find
`(u \cdot w)(2)` and
`(w \cdot u)(2)`.

The order doesn't matter in multiplication.

`(u \cdot w)(2)`

`u(2) \cdot w(2)`

`7 \cdot 2`

`14`

`(w \cdot u)(2)`

`w(2) \cdot u(2)`

`2 \cdot 7`

`14`

Now you might have meant composition which symbolized with an open circle, not a closed one.

`(u \circ w)(2)`

`u(w(2))`

`u(2)` since
`w(2)=2`

`2^2+3`

`4+3`

`7`

`(w \circ u)(2)`

`w(u(2))`

`w(7)` since
`u(2)=7`

`√(7+2)`

`√(9)`

`3`