Math Snap

STEP 1

1. We are given the functions $s(x) = 4x$ and $t(x) = 3x - 1$.
2. We need to find expressions for $(s \cdot t)(x)$ and $(s + t)(x)$.
3. We need to evaluate $(s - t)(-2)$.

STEP 2

1. Find the expression for $(s \cdot t)(x)$.
2. Find the expression for $(s + t)(x)$.
3. Evaluate $(s - t)(-2)$.

STEP 3

To find $(s \cdot t)(x)$, multiply the functions $s(x)$ and $t(x)$:
$$(s \cdot t)(x) = s(x) \cdot t(x) = (4x) \cdot (3x - 1)$$

STEP 4

Distribute to simplify the expression:
$$(s \cdot t)(x) = 4x \cdot 3x - 4x \cdot 1$$ $$(s \cdot t)(x) = 12x^2 - 4x$$

STEP 5

To find $(s + t)(x)$, add the functions $s(x)$ and $t(x)$:
$$(s + t)(x) = s(x) + t(x) = 4x + (3x - 1)$$

STEP 6

Simplify the expression:
$$(s + t)(x) = 4x + 3x - 1$$ $$(s + t)(x) = 7x - 1$$

STEP 7

To evaluate $(s - t)(-2)$, first find the expression for $(s - t)(x)$:
$$(s - t)(x) = s(x) - t(x) = 4x - (3x - 1)$$

STEP 8

Simplify the expression:
$$(s - t)(x) = 4x - 3x + 1$$ $$(s - t)(x) = x + 1$$

Substitute $x = -2$ into $(s - t)(x)$:
$$(s - t)(-2) = (-2) + 1$$ $$(s - t)(-2) = -1$$ The expressions and evaluation are:
$$\begin{array}{r} (s \cdot t)(x) = 12x^2 - 4x \\ (s + t)(x) = 7x - 1 \\ (s - t)(-2) = -1 \end{array}$$