Answer :
To find the value of [tex]\( f(-3) \)[/tex] for the function [tex]\( f(x) = x^3 - 2x^2 + 7x - 5 \)[/tex], we'll substitute [tex]\(-3\)[/tex] into the function in place of [tex]\( x \)[/tex] and then simplify step by step.
1. Substitute [tex]\(-3\)[/tex] into the function:
[tex]\[
f(-3) = (-3)^3 - 2(-3)^2 + 7(-3) - 5
\][/tex]
2. Calculate each term separately:
- Calculate [tex]\((-3)^3\)[/tex]:
[tex]\[
(-3)^3 = -27
\][/tex]
- Calculate [tex]\((-3)^2\)[/tex] and then multiply by [tex]\(-2\)[/tex]:
[tex]\[
(-3)^2 = 9 \quad \text{and} \quad -2 \times 9 = -18
\][/tex]
- Calculate [tex]\(7 \times (-3)\)[/tex]:
[tex]\[
7 \times (-3) = -21
\][/tex]
- The constant term is [tex]\(-5\)[/tex].
3. Combine all these values:
[tex]\[
f(-3) = -27 - 18 - 21 - 5
\][/tex]
4. Add them up:
- First, add [tex]\(-27\)[/tex] and [tex]\(-18\)[/tex]:
[tex]\[
-27 - 18 = -45
\][/tex]
- Then add [tex]\(-21\)[/tex]:
[tex]\[
-45 - 21 = -66
\][/tex]
- Finally, add [tex]\(-5\)[/tex]:
[tex]\[
-66 - 5 = -71
\][/tex]
So, the value of [tex]\( f(-3) \)[/tex] is [tex]\(-71\)[/tex]. The correct answer is [tex]\(\boxed{-71}\)[/tex].
1. Substitute [tex]\(-3\)[/tex] into the function:
[tex]\[
f(-3) = (-3)^3 - 2(-3)^2 + 7(-3) - 5
\][/tex]
2. Calculate each term separately:
- Calculate [tex]\((-3)^3\)[/tex]:
[tex]\[
(-3)^3 = -27
\][/tex]
- Calculate [tex]\((-3)^2\)[/tex] and then multiply by [tex]\(-2\)[/tex]:
[tex]\[
(-3)^2 = 9 \quad \text{and} \quad -2 \times 9 = -18
\][/tex]
- Calculate [tex]\(7 \times (-3)\)[/tex]:
[tex]\[
7 \times (-3) = -21
\][/tex]
- The constant term is [tex]\(-5\)[/tex].
3. Combine all these values:
[tex]\[
f(-3) = -27 - 18 - 21 - 5
\][/tex]
4. Add them up:
- First, add [tex]\(-27\)[/tex] and [tex]\(-18\)[/tex]:
[tex]\[
-27 - 18 = -45
\][/tex]
- Then add [tex]\(-21\)[/tex]:
[tex]\[
-45 - 21 = -66
\][/tex]
- Finally, add [tex]\(-5\)[/tex]:
[tex]\[
-66 - 5 = -71
\][/tex]
So, the value of [tex]\( f(-3) \)[/tex] is [tex]\(-71\)[/tex]. The correct answer is [tex]\(\boxed{-71}\)[/tex].
