Sure! Let's evaluate the function [tex]\((f - g)(6)\)[/tex] step by step for the given value of [tex]\(x\)[/tex].
1. Define the given functions:
[tex]\[
f(x) = 4x
\][/tex]
[tex]\[
g(x) = |x - 3|
\][/tex]
[tex]\[
h(x) = \frac{1}{x + 2}
\][/tex]
However, in this case, we are only concerned with [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] for evaluating [tex]\((f - g)(6)\)[/tex].
2. Calculate [tex]\(f(6)\)[/tex]:
[tex]\[
f(6) = 4 \cdot 6 = 24
\][/tex]
3. Calculate [tex]\(g(6)\)[/tex]:
[tex]\[
g(6) = |6 - 3| = 3
\][/tex]
4. Calculate [tex]\((f - g)(6)\)[/tex]:
[tex]\[
(f - g)(6) = f(6) - g(6) = 24 - 3 = 21
\][/tex]
Therefore, [tex]\((f - g)(6)\)[/tex] is [tex]\(21\)[/tex].
So,
[tex]\[
(f - g)(6) = 21
\][/tex]
