Question

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

Answer 1

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

Assumptions: $u(x)=x^2+3$ and $w(x)=\sqrt{x+2}$

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 $w(x)=\sqrt{x+2}$ or if $w(x)=\sqrt{x}+2$. Please let me know one way or the other.

Step-by-step explanation:

If we assume the functions are:

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

$w(x)=\sqrt{x+2}$

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

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

$u(2)=4+3$

$u(2)=7$

$w(2)=\sqrt{2+2}$

$w(2)=\sqrt{4}$

$w(2)=2$

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 $u(2)=7$

$\sqrt{7+2}$

$\sqrt{9}$

$3$