To determine which input values satisfy the equation [tex]\( f(x) = 2 \)[/tex] for the function [tex]\( f(x) = x - 6 \)[/tex], we can follow these steps for each given value:
1. Start by evaluating [tex]\( f(x) \)[/tex] for each value given:
- For [tex]\( x = -7 \)[/tex]:
[tex]\[
f(-7) = -7 - 6 = -13
\][/tex]
Since [tex]\(-13 \neq 2\)[/tex], [tex]\( x = -7 \)[/tex] is not a solution.
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 0 - 6 = -6
\][/tex]
Since [tex]\(-6 \neq 2\)[/tex], [tex]\( x = 0 \)[/tex] is not a solution.
- For [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = 4 - 6 = -2
\][/tex]
Since [tex]\(-2 \neq 2\)[/tex], [tex]\( x = 4 \)[/tex] is not a solution.
2. After testing all given values, none of them satisfy the condition [tex]\( f(x) = 2 \)[/tex].
Therefore, the correct answer is:
- D: None of the above
