Questions: The functions (f) and (g) are defined as follows. [ f(x)=-3 x-1 quad g(x)=4 x^2-x ] Find (f(4)) and (g(-4)). Simplify your answers as much as possible. [ f(4)=-13 ] [ g(-4)=68 ]

Transcript text: The functions $f$ and $g$ are defined as follows. \[ f(x)=-3 x-1 \quad g(x)=4 x^{2}-x \] Find $f(4)$ and $g(-4)$. Simplify your answers as much as possible. \[ \begin{array}{l} f(4)=-13 \\ g(-4)=68 \end{array} \]

Solution

Solution Steps

To find $ f(4) $ and $ g(-4) $, we need to substitute the given values into the respective function definitions. For $ f(x) = -3x - 1 $, substitute $ x = 4 $ to find $ f(4) $. For $ g(x) = 4x^2 - x $, substitute $ x = -4 $ to find $ g(-4) $.

Step 1: Evaluate $ f(4) $

To find $ f(4) $, substitute $ x = 4 $ into the function $ f(x) = -3x - 1 $.

\[ f(4) = -3(4) - 1 = -12 - 1 = -13 \]

Step 2: Evaluate $ g(-4) $

To find $ g(-4) $, substitute $ x = -4 $ into the function $ g(x) = 4x^2 - x $.

\[ g(-4) = 4(-4)^2 - (-4) = 4(16) + 4 = 64 + 4 = 68 \]