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

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

Solution

Solution Steps

To find $ f(-2) $ and $ g(-4) $, we need to substitute $ x = -2 $ into the function $ f(x) = 4x - 1 $ and $ x = -4 $ into the function $ g(x) = 2x^2 - 3x $. This will give us the values of the functions at these specific points.

Step 1: Evaluate $ f(-2) $

To find $ f(-2) $, substitute $ x = -2 $ into the function $ f(x) = 4x - 1 $.

\[ f(-2) = 4(-2) - 1 = -8 - 1 = -9 \]

Step 2: Evaluate $ g(-4) $

To find $ g(-4) $, substitute $ x = -4 $ into the function $ g(x) = 2x^2 - 3x $.

\[ g(-4) = 2(-4)^2 - 3(-4) = 2(16) + 12 = 32 + 12 = 44 \]