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)= - QAmmunity.org

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)=

asked Oct 7, 2020 1.5k views

1 Answer

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.

$(u \cdot w)(2)$

$u(2) \cdot w(2)$

$7 \cdot 2$

$(w \cdot u)(2)$

$w(2) \cdot u(2)$

$2 \cdot 7$

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

$(w \circ u)(2)$

w(u(2))

w(7) since
u(2)=7

√(7+2)

√(9)

Briba answered Oct 13, 2020

by Briba

8.3k points

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