uppose that the functions $$ r $$ and $$ s $$ are defined for all real numbers $$ x $$ as follows. $$ \begin{array}{l}r(x)=3 x \ s(x)=4 x^{2} \ \text { Vrite the expressions for }(r-s)(x) \text { and }(r \cdot s)(x) \text { and evaluate }(r+s)(-2) \text {. } \ \begin{array}{l}(r-s)(x)=\square \ (r+s)(x)=\square\end{array}\end{array} . \begin{array}{l}(r+s)(-2)=\square\end{array} $$

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1. The function $$ r $$ is given by
   $$
   r(x) = 3x.
   $$
   The function $$ s $$ is given by
   $$
   s(x) = 4x^2.
   $$

2. To find $$(r-s)(x)$$, subtract $$ s(x) $$ from $$ r(x) $$:
   $$
   (r-s)(x) = r(x) - s(x) = 3x - 4x^2.
   $$

3. To find $$(r \cdot s)(x)$$, multiply $$ r(x) $$ by $$ s(x) $$:
   $$
   (r \cdot s)(x) = r(x) \cdot s(x) = 3x \cdot 4x^2 = 12x^3.
   $$

4. Finally, to evaluate $$(r+s)(-2)$$, first find $$(r+s)(x)$$:
   $$
   (r+s)(x) = r(x) + s(x) = 3x + 4x^2.
   $$
   Now substitute $$ x = -2 $$:
   $$
   (r+s)(-2) = 3(-2) + 4(-2)^2 = -6 + 4(4) = -6 + 16 = 10.
   $$

Thus, 
- $$(r-s)(x) = 3x - 4x^2$$,
- $$(r \cdot s)(x) = 12x^3$$,
- $$(r+s)(-2) = 10$$.
$$ \begin{array}{l} (r-s)(x) = 3x - 4x^2 \ (r \cdot s)(x) = 12x^3 \ (r+s)(-2) = 10 \end{array} $$

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

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