To find [tex]\( f(-1) \)[/tex] for the given function [tex]\( f(x) = 3x^2 - 2x - 7 \)[/tex], you need to substitute [tex]\( x = -1 \)[/tex] into the function and simplify:
1. Substitution: Start by substituting [tex]\( x = -1 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-1) = 3(-1)^2 - 2(-1) - 7
\][/tex]
2. Evaluate [tex]\( (-1)^2 \)[/tex]: Calculate the square of [tex]\(-1\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
3. Multiply by 3: Multiply 3 by the result of [tex]\((-1)^2\)[/tex]:
[tex]\[
3 \times 1 = 3
\][/tex]
4. Evaluate [tex]\(- 2(-1)\)[/tex]: Calculate [tex]\( -2 \times (-1) \)[/tex]:
[tex]\[
-2 \times (-1) = 2
\][/tex]
5. Combine the terms: Now, add all the terms together:
[tex]\[
3 + 2 - 7
\][/tex]
6. Simplify: Perform the arithmetic operation:
[tex]\[
3 + 2 = 5
\][/tex]
[tex]\[
5 - 7 = -2
\][/tex]
Therefore, the value of [tex]\( f(-1) \)[/tex] is:
[tex]\[
f(-1) = -2
\][/tex]
