To find the values of [tex]\(f(-4)\)[/tex] and [tex]\(g(-6)\)[/tex] given the functions [tex]\(f(x) = -3x^3 - 2\)[/tex] and [tex]\(g(x) = 3x - 3\)[/tex], let's proceed step-by-step.
### Step 1: Calculate [tex]\( f(-4) \)[/tex]
The function [tex]\( f(x) \)[/tex] is defined as:
[tex]\[ f(x) = -3x^3 - 2 \][/tex]
Substitute [tex]\( x = -4 \)[/tex]:
[tex]\[ f(-4) = -3(-4)^3 - 2 \][/tex]
Calculate [tex]\( (-4)^3 \)[/tex]:
[tex]\[ (-4)^3 = -64 \][/tex]
Now, substitute [tex]\( -64 \)[/tex] back into the equation:
[tex]\[ f(-4) = -3(-64) - 2 \][/tex]
Multiply [tex]\( -3 \)[/tex] by [tex]\( -64 \)[/tex]:
[tex]\[ -3 \times -64 = 192 \][/tex]
Finally, subtract 2:
[tex]\[ f(-4) = 192 - 2 = 190 \][/tex]
So, [tex]\( f(-4) = 190 \)[/tex].
### Step 2: Calculate [tex]\( g(-6) \)[/tex]
The function [tex]\( g(x) \)[/tex] is defined as:
[tex]\[ g(x) = 3x - 3 \][/tex]
Substitute [tex]\( x = -6 \)[/tex]:
[tex]\[ g(-6) = 3(-6) - 3 \][/tex]
Calculate [tex]\( 3 \times -6 \)[/tex]:
[tex]\[ 3 \times -6 = -18 \][/tex]
Finally, subtract 3:
[tex]\[ g(-6) = -18 - 3 = -21 \][/tex]
So, [tex]\( g(-6) = -21 \)[/tex].
### Conclusion
After calculating both expressions, we find:
[tex]\[ f(-4) = 190 \][/tex]
[tex]\[ g(-6) = -21 \][/tex]
Thus, the values are:
[tex]\[ f(-4) = 190 \][/tex]
[tex]\[ g(-6) = -21 \][/tex]
