Question

the functions f and g are defined as follows.
$f(x)=3x - 1$ $g(x)=2x^{3}+6$
find $f(-5)$ and $g(-4)$.
simplify your answers as much as possible.

Explanation:

Step1: Find \( f(-5) \)

Substitute \( x = -5 \) into \( f(x) = 3x - 1 \).
\( f(-5) = 3\times(-5) - 1 \)

Step2: Calculate \( f(-5) \)

First, calculate \( 3\times(-5) = -15 \), then \( -15 - 1 = -16 \). So \( f(-5) = -16 \).

Step3: Find \( g(-4) \)

Substitute \( x = -4 \) into \( g(x) = 2x^3 + 6 \).
\( g(-4) = 2\times(-4)^3 + 6 \)

Step4: Calculate \( g(-4) \)

First, calculate \( (-4)^3 = -64 \), then \( 2\times(-64) = -128 \), and finally \( -128 + 6 = -122 \). So \( g(-4) = -122 \).

Answer:

\( f(-5) = -16 \)
\( g(-4) = -122 \)