To determine which values in the domain make the function [tex]\( f(x) = 0 \)[/tex], we need to evaluate the function at each of the given points and check whether the function equals zero.
We are given the domain values [tex]\( x = -3 \)[/tex], [tex]\( x = 0 \)[/tex], and [tex]\( x = 1 \)[/tex].
Let's evaluate the function [tex]\( f(x) \)[/tex] at these values:
1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = -3 \)[/tex]:
- Plug in [tex]\( x = -3 \)[/tex] into the function [tex]\( f(x) \)[/tex].
- Calculate [tex]\( f(-3) \)[/tex].
2. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 0 \)[/tex]:
- Plug in [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) \)[/tex].
- Calculate [tex]\( f(0) \)[/tex].
- Check if [tex]\( f(0) \)[/tex] equals zero.
3. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 1 \)[/tex]:
- Plug in [tex]\( x = 1 \)[/tex] into the function [tex]\( f(x) \)[/tex].
- Calculate [tex]\( f(1) \)[/tex].
- Check if [tex]\( f(1) \)[/tex] equals zero.
After performing these evaluations, we find the results as follows:
- For [tex]\( x = -3 \)[/tex], [tex]\( f(-3) \)[/tex] does not equal 0.
- For [tex]\( x = 0 \)[/tex], [tex]\( f(0) \)[/tex] equals 0.
- For [tex]\( x = 1 \)[/tex], [tex]\( f(1) \)[/tex] equals 0.
So, the values in the domain that make [tex]\( f(x) \)[/tex] equal to 0 are [tex]\( x = 0 \)[/tex] and [tex]\( x = 1 \)[/tex].
Therefore, the values in the domain where [tex]\( f(x) = 0 \)[/tex] are:
[tex]\[ x = 0 \][/tex]
[tex]\[ x = 1 \][/tex]
