Question

suppose that the functions u and w are defined as follows.
u(x) = -x - 1
w(x) = 2x² - 2
find the following.
(w ∘ u)(-4) =
(u ∘ w)(-4) =

Explanation:

Step1: Define product function

$(w \cdot u)(x) = w(x) \cdot u(x)$

Step2: Substitute $x=-4$ into $u(x)$

$u(-4) = -(-4) - 1 = 4 - 1 = 3$

Step3: Substitute $x=-4$ into $w(x)$

$w(-4) = 2(-4)^2 - 2 = 2(16) - 2 = 32 - 2 = 30$

Step4: Calculate $(w \cdot u)(-4)$

$(w \cdot u)(-4) = w(-4) \cdot u(-4) = 30 \times 3 = 90$

Step5: Calculate $(u \cdot w)(-4)$

Multiplication is commutative, so $(u \cdot w)(-4) = (w \cdot u)(-4) = 90$

Answer:

$(w \cdot u)(-4) = 90$
$(u \cdot w)(-4) = 90$