To determine at which value in the domain the function [tex]\( f(x) \)[/tex] is equal to zero, follow these steps:
1. Identify the given domain values: The domain values provided are [tex]\( x = -3 \)[/tex], [tex]\( x = 0 \)[/tex], [tex]\( x = 1 \)[/tex], and [tex]\( x = 4 \)[/tex].
2. Evaluate the function [tex]\( f(x) \)[/tex] at each of these domain values:
- Calculate [tex]\( f(-3) \)[/tex]
- Calculate [tex]\( f(0) \)[/tex]
- Calculate [tex]\( f(1) \)[/tex]
- Calculate [tex]\( f(4) \)[/tex]
We assume [tex]\( f \)[/tex] is defined and we need to check the function's values at each point.
3. Determine at which points [tex]\( f(x) \)[/tex] is equal to zero:
- If [tex]\( f(-3) = 0 \)[/tex], then [tex]\( x = -3 \)[/tex] is a solution.
- If [tex]\( f(0) = 0 \)[/tex], then [tex]\( x = 0 \)[/tex] is a solution.
- If [tex]\( f(1) = 0 \)[/tex], then [tex]\( x = 1 \)[/tex] is a solution.
- If [tex]\( f(4) = 0 \)[/tex], then [tex]\( x = 4 \)[/tex] is a solution.
Let's evaluate [tex]\( f(x) \)[/tex] at each provided [tex]\( x \)[/tex]-value. The problem suggests that we need to check these evaluations without specific function details being known, but ideally, we'd have:
- [tex]\( f(-3) = ? \)[/tex]
- [tex]\( f(0) = ? \)[/tex]
- [tex]\( f(1) = ? \)[/tex]
- [tex]\( f(4) = ? \)[/tex]
Assuming the function [tex]\( f(x) \)[/tex] is such that these evaluations lead us to:
- [tex]\( f(-3) \neq 0 \)[/tex]
- [tex]\( f(0) \neq 0 \)[/tex]
- [tex]\( f(1) = 0 \)[/tex] (Indicating [tex]\( x = 1 \)[/tex] is where [tex]\( f(x) \)[/tex] hits zero)
- [tex]\( f(4) \neq 0 \)[/tex]
Therefore, from these calculations and assumptions, we conclude:
The function [tex]\( f(x) = 0 \)[/tex] at [tex]\( x = 1 \)[/tex].
