Certainly! Let's solve the given function [tex]\( f(x) = x^3 - 3x^2 + 4x - 12 \)[/tex] and evaluate it at [tex]\( x = 3 \)[/tex].
### Step-by-Step Solution:
1. Identify the function and the value of [tex]\( x \)[/tex]:
- We are given the function [tex]\( f(x) = x^3 - 3x^2 + 4x - 12 \)[/tex].
- We are also given the value [tex]\( x = 3 \)[/tex].
2. Substitute [tex]\( x = 3 \)[/tex] into the function:
- Replace every occurrence of [tex]\( x \)[/tex] in the function [tex]\( f(x) \)[/tex] with [tex]\( 3 \)[/tex].
So we get:
[tex]\[
f(3) = 3^3 - 3(3^2) + 4(3) - 12
\][/tex]
3. Calculate each term step-by-step:
- First term: [tex]\( 3^3 = 27 \)[/tex]
- Second term: [tex]\( -3(3^2) = -3(9) = -27 \)[/tex]
- Third term: [tex]\( 4(3) = 12 \)[/tex]
- Fourth term: [tex]\( -12 \)[/tex]
4. Combine the results:
- Now, add and subtract these results step-by-step:
[tex]\[
f(3) = 27 - 27 + 12 - 12
\][/tex]
5. Simplify the expression:
- Combining the terms, we get:
[tex]\[
27 - 27 = 0
\][/tex]
- Next, combine:
[tex]\[
12 - 12 = 0
\][/tex]
- Finally:
[tex]\[
0 + 0 = 0
\][/tex]
### Final Answer:
[tex]\[
f(3) = 0
\][/tex]
So, when [tex]\( x = 3 \)[/tex], the value of the function [tex]\( f(x) = x^3 - 3x^2 + 4x - 12 \)[/tex] is [tex]\( 0 \)[/tex].
