Question

Given u(x) = -2x + 2 and w(x) = -x² - 1, find the following.

(u • w)(-5) =
a) -28
b) -18
c) -15
d) -12

(w • u)(-5) =
a) -28
b) -18
c) -15
d) -12

Answer 1

The product (u • w)(-5) equals -312. The correct answer is not listed among the provided choices, as there seems to be a typo or miscalculation in the options given to the student.

Step-by-step explanation:

The student has asked to find the product of two functions evaluated at a particular point. Specifically, they need to calculate the product of u(x) = -2x + 2 and w(x) = -x² - 1, at the point where x = -5.

First, evaluate u at x = -5:

• u(-5) = -2(-5) + 2 = 10 + 2 = 12

Then, evaluate w at x = -5:

• w(-5) = -(-5)² - 1 = -25 - 1 = -26

Finally, multiply the results from both functions:

• (u • w)(-5) = u(-5) • w(-5) = 12 • (-26) = -312

The order of multiplication doesn't change the result, hence (w • u)(-5) is also equal to -312,