Question

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

u(x)=x+1
w (x) = -2x² +2
Find the following.
(wou) (2) =
(uw) (2) =
X
Ś

Answer 1

To compute (wou)(2) and (uw)(2), we evaluate u(2), apply w to that result to get (wou)(2) = -16, then evaluate w(2), and apply u to get (uw)(2) = -5.

Step-by-step explanation:

The question requires us to compose two functions u(x) and w(x), and then evaluate the compositions at x=2. The notation (wou)(2) represents the function w composed with function u, evaluated at 2; meaning, we first apply u to 2, and then apply w to the result.

Conversely, (uw)(2) means we first apply w to 2, and then apply u. Here are the steps to find the values:

Step 1: Evaluate u(2)
u(x) = x + 1 so u(2)

= 2 + 1

= 3.

Step 2: Compute (wou)(2)

Now we apply w to the result of u(2):
w(3) = -2(3)² + 2

= -2(9) + 2

= -18 + 2

= -16.

Therefore, (wou)(2) = -16.

Step 3: Evaluate w(2)
w(x) = -2x² + 2 so w(2)

= -2(2)² + 2

= -2(4) + 2

= -8 + 2

= -6.

Step 4: Compute (uw)(2)

Finally, we apply u to the result of w(2):
u(-6) = -6 + 1

= -5.

Therefore, (uw)(2) = -5.