Select all input values for which [tex]f(x)=2[/tex].

Choose all answers that apply:

A. [tex]x=-7[/tex]

B. [tex]x=0[/tex]

C. [tex]x=4[/tex]

D. None of the above



Answer :

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