Question

suppose that the functions u and w are defined as follows.
$u(x) = 2x - 1$
$w(x) = -2x^2$
find the following.
$(u \circ w)(5) = -450$
$(w \circ u)(5) = -450$

Explanation:

Step1: Define product function

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

Step2: Substitute x=5 into u(x)

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

Step3: Substitute x=5 into w(x)

$w(5) = -2(5)^2 = -50$

Step4: Calculate $(u \cdot w)(5)$

$(u \cdot w)(5) = 9 \times (-50) = -450$

Step5: Calculate $(w \cdot u)(5)$

$(w \cdot u)(5) = w(5) \cdot u(5) = -50 \times 9 = -450$

Answer:

$(u \cdot w)(5) = -450$
$(w \cdot u)(5) = -450$