Questions: The functions (f) and (g) are defined as follows. (f(x)=3 x^2-3 x) and (g(x)=4 x+4). Find (f(-2)) and (g(-3)). Simplify your answers as much as possible. (f(-2)=) (g(-3)=)

Transcript text: The functions $f$ and $g$ are defined as follows. \[ f(x)=3 x^{2}-3 x \quad g(x)=4 x+4 \] Find $f(-2)$ and $g(-3)$ Simplify your answers as much as possible. \[ f(-2)= \] $\square$ \[ g(-3)= \] $\square$

Solution

Solution Steps

To find $ f(-2) $, substitute $-2$ into the function $ f(x) = 3x^2 - 3x $ and evaluate. Similarly, to find $ g(-3) $, substitute $-3$ into the function $ g(x) = 4x + 4 $ and evaluate.

Step 1: Evaluate $ f(-2) $

To find $ f(-2) $, we substitute $-2$ into the function $ f(x) = 3x^2 - 3x $: \[ f(-2) = 3(-2)^2 - 3(-2) = 3(4) + 6 = 12 + 6 = 18 \]

Step 2: Evaluate $ g(-3) $

Next, we find $ g(-3) $ by substituting $-3$ into the function $ g(x) = 4x + 4 $: \[ g(-3) = 4(-3) + 4 = -12 + 4 = -8 \]