Ask Question
27 August, 22:51

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

u (x) = - x - 2

w (x) = 2 x^2

Find the following.

(u o w) (4) = __

(w o u) (4) = __

I really have no idea what this is

+2
Answers (1)
  1. 28 August, 00:01
    0
    That funky circle in the middle is the composition of the function. It asks you to take a function as an input and to yield an output that's another function. It's one of the five function operations, along with adding, subtracting, multiplying, and dividing.

    When you compose, you might find the notation w (u (x)) easier to understand. It's saying evaluate u then evaluate w.

    For our functions, the compositions are:

    u (w (x)) = u (2x²) = - (2x²) - 2 = - 2x² - 2

    w (u (x)) = w (-x - 2) = 2 (-x - 2) ² = 2 (x² + 4x + 4) = = 2x² + 8x + 8

    Now we evaluate each composition at 4.

    u (w (4)) = - 2 (4²) - 2 = - 2 (16) - 2 = - 32 - 2 = - 34

    w (u (4)) = - 2 (2²) + 8 (2) + 8 = - 2 (4) + 16 + 8 = - 8 + 16 + 8 = 16.

    Thus, u (w (4)) = - 34 and w (u (4)) = 16.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Suppose that the function u and w are defined as follows. u (x) = - x - 2 w (x) = 2 x^2 Find the following. (u o w) (4) = __ (w o u) (4) = ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers