Sure! Let's solve the problem step-by-step.
Given the functions:
[tex]\[ f(x) = 8 - 10x \][/tex]
[tex]\[ g(x) = 5x + 4 \][/tex]
We need to find the value of [tex]\((fg)(-2)\)[/tex], which means we need to evaluate the composite function [tex]\( f(g(-2)) \)[/tex].
Step 1: Evaluate [tex]\( g(-2) \)[/tex]
Substitute [tex]\( x = -2 \)[/tex] into the function [tex]\( g(x) = 5x + 4 \)[/tex]:
[tex]\[ g(-2) = 5(-2) + 4 \][/tex]
Perform the arithmetic operations:
[tex]\[ g(-2) = -10 + 4 \][/tex]
[tex]\[ g(-2) = -6 \][/tex]
Step 2: Evaluate [tex]\( f(g(-2)) \)[/tex] which is [tex]\( f(-6) \)[/tex]
Now we substitute [tex]\( x = -6 \)[/tex] into the function [tex]\( f(x) = 8 - 10x \)[/tex]:
[tex]\[ f(-6) = 8 - 10(-6) \][/tex]
Perform the arithmetic operations:
[tex]\[ f(-6) = 8 + 60 \][/tex]
[tex]\[ f(-6) = 68 \][/tex]
Therefore, the value of [tex]\( (fg)(-2) \)[/tex] is:
[tex]\[ \boxed{68} \][/tex]
