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

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

Solution

Solution Steps

To solve for $ f(4) $ and $ g(-3) $, we need to substitute $ x = 4 $ into the function $ f(x) $ and $ x = -3 $ into the function $ g(x) $. Then, we will simplify the expressions to find the values.

Step 1: Evaluate $ f(4) $

To find $ f(4) $, we substitute $ x = 4 $ into the function $ f(x) = -4x + 4 $: \[ f(4) = -4(4) + 4 = -16 + 4 = -12 \]

Step 2: Evaluate $ g(-3) $

To find $ g(-3) $, we substitute $ x = -3 $ into the function $ g(x) = -2x^3 - 5 $: \[ g(-3) = -2(-3)^3 - 5 = -2(-27) - 5 = 54 - 5 = 49 \]