Question

suppose that the functions u and w are defined as follows.
u(x) = 2x - 1
w(x) = -2x²
find the following.
(u ⋅ w)(5) =
(w ⋅ u)(5) =

Explanation:

Step1: Define function composition

$(u \circ w)(x) = u(w(x))$, $(w \circ u)(x) = w(u(x))$

Step2: Compute $w(5)$ first

$w(5) = -2(5)^2 = -2 \times 25 = -50$

Step3: Compute $(u \circ w)(5)$

$u(w(5)) = u(-50) = 2(-50) - 1 = -100 - 1 = -101$

Step4: Compute $u(5)$ first

$u(5) = 2(5) - 1 = 10 - 1 = 9$

Step5: Compute $(w \circ u)(5)$

$w(u(5)) = w(9) = -2(9)^2 = -2 \times 81 = -162$

Answer:

$(u \cdot w)(5) = -101$
$(w \cdot u)(5) = -162$