To find [tex]\( f(-3) \)[/tex] and [tex]\( g(6) \)[/tex] using the given functions:
First, let's determine [tex]\( f(-3) \)[/tex].
The function [tex]\( f(x) \)[/tex] is defined as:
[tex]\[ f(x) = 2x^2 - 3x \][/tex]
Substitute [tex]\( x = -3 \)[/tex] into the function:
[tex]\[ f(-3) = 2(-3)^2 - 3(-3) \][/tex]
Calculate the value:
[tex]\[ (-3)^2 = 9 \][/tex]
[tex]\[ 2 \cdot 9 = 18 \][/tex]
[tex]\[ -3 \cdot -3 = 9 \][/tex]
So:
[tex]\[ f(-3) = 18 + 9 = 27 \][/tex]
Therefore:
[tex]\[ f(-3) = 27 \][/tex]
Next, let's determine [tex]\( g(6) \)[/tex].
The function [tex]\( g(x) \)[/tex] is defined as:
[tex]\[ g(x) = -4x + 2 \][/tex]
Substitute [tex]\( x = 6 \)[/tex] into the function:
[tex]\[ g(6) = -4 \cdot 6 + 2 \][/tex]
Calculate the value:
[tex]\[ -4 \cdot 6 = -24 \][/tex]
So:
[tex]\[ g(6) = -24 + 2 = -22 \][/tex]
Therefore:
[tex]\[ g(6) = -22 \][/tex]
To summarize our results:
[tex]\[ f(-3) = 27 \][/tex]
[tex]\[ g(6) = -22 \][/tex]
