Suppose that the functions $$ r $$ and $$ s $$ are defined for all real numbers $$ x $$ as follows. $$ \begin{array}{l} r(x)=4 x-5 \ s(x)=6 x \end{array} $$ Write the expressions for $$ (s-r)(x) $$ and $$ (s+r)(x) $$ and evaluate $$ (s \cdot r)(2) $$. $$ \begin{array}{c} (s-r)(x)= \ (s+r)(x)= \ (s \cdot r)(2)= \end{array} $$

Question

UpStudy AI · Accepted Answer

We are given
$$
r(x)=4x-5 \quad \text{and} \quad s(x)=6x.
$$

**Step 1. Compute $$(s - r)(x)$$:**

$$
(s - r)(x)=s(x)-r(x)=6x-(4x-5)
$$
Distribute the negative sign:
$$
=6x-4x+5=2x+5.
$$

**Step 2. Compute $$(s + r)(x)$$:**

$$
(s + r)(x)=s(x)+r(x)=6x+(4x-5)
$$
Combine like terms:
$$
=6x+4x-5=10x-5.
$$

**Step 3. Evaluate $$(s \cdot r)(2)$$:**

First, find $$s(2)$$ and $$r(2)$$:
$$
s(2)=6(2)=12,
$$
$$
r(2)=4(2)-5=8-5=3.
$$
Now, multiply these values:
$$
(s \cdot r)(2)=s(2)r(2)=12\cdot3=36.
$$

Thus, the final answers are:

$$
\begin{array}{c}
(s - r)(x)=2x+5 \
(s + r)(x)=10x-5 \
(s \cdot r)(2)=36
\end{array}
$$
$$ \begin{array}{c} (s - r)(x) = 2x + 5 \ (s + r)(x) = 10x - 5 \ (s \cdot r)(2) = 36 \end{array} $$

Suppose that the functions and are defined for all real numbers as follows.

Write the expressions for and and evaluate .

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions

Suppose that the functions and are defined for all real numbers as follows. Write the expressions for and and evaluate .