To determine the value of [tex]\( f(-x) \)[/tex] given the function [tex]\( f(x) = 3x^2 - 4 \)[/tex], we need to substitute [tex]\(-x\)[/tex] into the function in place of [tex]\(x\)[/tex].
1. Start with the given function:
[tex]\[
f(x) = 3x^2 - 4
\][/tex]
2. Substitute [tex]\(-x\)[/tex] for [tex]\(x\)[/tex] in the function:
[tex]\[
f(-x) = 3(-x)^2 - 4
\][/tex]
3. Evaluate the expression inside the function:
[tex]\[
(-x)^2 = x^2
\][/tex]
So,
[tex]\[
f(-x) = 3x^2 - 4
\][/tex]
Therefore, [tex]\( f(-x) \)[/tex] simplifies to:
[tex]\[
f(-x) = 3x^2 - 4
\][/tex]
Comparing this result with the given choices:
- Choice (A): [tex]\( f(x-1) \)[/tex]
- Choice (B): [tex]\( -f(x) \)[/tex]
It is clear that neither [tex]\( f(x-1) \)[/tex] nor [tex]\( -f(x) \)[/tex] matches our result [tex]\( f(-x) = 3x^2 - 4 \)[/tex].
Hence, [tex]\( f(-x) = 3x^2 - 4 \)[/tex] is consistent with the given problem but does not match options (A) or (B) as given.
