Suppose that the functions $$ u $$ and $$ w $$ are defined as follows. $$ \left.\qquad \begin{array}{l}u(x)=-2 x \ w(x)=-4 x-1 \ ext { Find the following. } \ \begin{array}{l}(w \circ u)(1)=\square \ (u \circ w)(1)=\square\end{array}\end{array} ight) $$.

Question

Suppose that the functions $$ u $$ and $$ w $$ are defined as follows. $$ \left.\qquad \begin{array}{l}u(x)=-2 x \ w(x)=-4 x-1 \ 	ext { Find the following. } \ \begin{array}{l}(w \circ u)(1)=\square \ (u \circ w)(1)=\square\end{array}\end{array}ight) $$.

UpStudy AI · Accepted Answer

We are given the functions
$$
u(x) = -2x \quad \text{and} \quad w(x) = -4x - 1.
$$

**Step 1: Compute $$(w \circ u)(1)$$**

1. Calculate $$ u(1) $$:
   $$
   u(1) = -2 \cdot 1 = -2.
   $$

2. Substitute $$ u(1) $$ into $$ w(x) $$ to find $$ w(u(1)) $$:
   $$
   w(-2) = -4(-2) - 1 = 8 - 1 = 7.
   $$

Thus, 
$$
(w \circ u)(1) = 7.
$$

---

**Step 2: Compute $$(u \circ w)(1)$$**

1. Calculate $$ w(1) $$:
   $$
   w(1) = -4 \cdot 1 - 1 = -4 - 1 = -5.
   $$

2. Substitute $$ w(1) $$ into $$ u(x) $$ to find $$ u(w(1)) $$:
   $$
   u(-5) = -2(-5) = 10.
   $$

Thus,
$$
(u \circ w)(1) = 10.
$$

---

Answers:
$$
(w \circ u)(1)=7 \quad \text{and} \quad (u \circ w)(1)=10.
$$
$$ (w \circ u)(1) = 7 \quad \text{and} \quad (u \circ w)(1) = 10 $$

Suppose that the functions and are defined as follows.
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