Suppose that the functions $$ s $$ and $$ t $$ are defined for all real numbers $$ x $$ as follows. $$ \begin{array}{l}s(x)=x-5 \ t(x)=3 x-4 \ (t \cdot s)(x)=\square \ (t+s)(x)=\square \ (t-s)(2)=\square\end{array} $$ Write the expressions for $$ (t \cdot s)(x) $$ and $$ (t+s)(x) $$ and evaluate $$ (t-s)(2) $$.

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1. Given:
   - $$ s(x) = x - 5 $$
   - $$ t(x) = 3x - 4 $$

2. To find $$ (t \cdot s)(x) $$, we multiply $$ t(x) $$ by $$ s(x) $$:
   $$
   (t \cdot s)(x) = t(x) \cdot s(x) = (3x - 4)(x - 5)
   $$
   Expanding the product:
   $$
   (3x - 4)(x - 5) = 3x \cdot x + 3x \cdot (-5) - 4 \cdot x - 4 \cdot (-5)
   $$
   Simplify each term:
   $$
   = 3x^2 - 15x - 4x + 20 = 3x^2 - 19x + 20
   $$

3. To find $$ (t+s)(x) $$, we add $$ t(x) $$ and $$ s(x) $$:
   $$
   (t+s)(x) = t(x) + s(x) = (3x - 4) + (x - 5)
   $$
   Combine like terms:
   $$
   = 3x + x - 4 - 5 = 4x - 9
   $$

4. To evaluate $$ (t-s)(2) $$, we first find the expression for $$ (t-s)(x) $$:
   $$
   (t-s)(x) = t(x) - s(x) = (3x - 4) - (x - 5)
   $$
   Simplify the expression:
   $$
   = 3x - 4 - x + 5 = 2x + 1
   $$
   Then substitute $$ x = 2 $$:
   $$
   (t-s)(2) = 2(2) + 1 = 4 + 1 = 5
   $$

Thus, the answers are:
- $$ (t \cdot s)(x) = 3x^2 - 19x + 20 $$
- $$ (t+s)(x) = 4x - 9 $$
- $$ (t-s)(2) = 5 $$
$$ (t \cdot s)(x) = 3x^2 - 19x + 20 $$, $$ (t+s)(x) = 4x - 9 $$, and $$ (t-s)(2) = 5 $$.

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

Write the expressions for and and evaluate .

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