Questions: The functions (f) and (g) are defined as follows. [f(x)=3 x^3+5 quad g(x)=2 x+4] Find (f(-4)) and (g(-7)) Simplify your answers as much as possible. [f(-4)=square g(-7)=square]

The functions (f) and (g) are defined as follows.
[f(x)=3 x^3+5 quad g(x)=2 x+4]

Find (f(-4)) and (g(-7))
Simplify your answers as much as possible.
[f(-4)=square g(-7)=square]

Transcript text: The functions $f$ and $g$ are defined as follows. \[ f(x)=3 x^{3}+5 \quad g(x)=2 x+4 \] Find $f(-4)$ and $g(-7)$ Simplify your answers as much as possible. \[ \begin{array}{l} f(-4)=\square \\ g(-7)=\square \end{array} \]

Solution

Solution Steps

To solve for $ f(-4) $ and $ g(-7) $ using the given functions $ f(x) = 3x^3 + 5 $ and $ g(x) = 2x + 4 $, we need to substitute $ x $ with $-4$ in $ f(x) $ and $-7$ in $ g(x) $, and then simplify the results.

Step 1: Evaluate $ f(-4) $

To find $ f(-4) $, we substitute $-4$ into the function $ f(x) = 3x^3 + 5 $:

\[ f(-4) = 3(-4)^3 + 5 \] Calculating $(-4)^3$:

\[ (-4)^3 = -64 \] Now substituting back:

\[ f(-4) = 3(-64) + 5 = -192 + 5 = -187 \]

Step 2: Evaluate $ g(-7) $

Next, we find $ g(-7) $ by substituting $-7$ into the function $ g(x) = 2x + 4 $:

\[ g(-7) = 2(-7) + 4 \] Calculating $2(-7)$:

\[ 2(-7) = -14 \] Now substituting back:

\[ g(-7) = -14 + 4 = -10 \]