To solve [tex]\((g - f)(2)\)[/tex], we need to break down the problem step by step.
1. Identify the given functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
f(x) = 2x + 8
\][/tex]
[tex]\[
g(x) = x^2 + 2x - 8
\][/tex]
2. Determine [tex]\( g(x) - f(x) \)[/tex]:
[tex]\[
g(x) - f(x) = (x^2 + 2x - 8) - (2x + 8)
\][/tex]
Simplify the expression by distributing and combining like terms:
[tex]\[
g(x) - f(x) = x^2 + 2x - 8 - 2x - 8
\][/tex]
[tex]\[
g(x) - f(x) = x^2 - 16
\][/tex]
3. Evaluate the simplified expression at [tex]\( x = 2 \)[/tex]:
[tex]\[
(g - f)(2) = 2^2 - 16
\][/tex]
[tex]\[
(g - f)(2) = 4 - 16
\][/tex]
[tex]\[
(g - f)(2) = -12
\][/tex]
Thus, the result of the operation [tex]\( (g - f)(2) \)[/tex] is:
[tex]\[
(g-f)(2) = -12
\][/tex]
