Answer :
To find the value of [tex]\( f(-3) \)[/tex] for the function [tex]\( f(x) = x^3 - 2x^2 + 7x - 5 \)[/tex], we need to substitute [tex]\(-3\)[/tex] into the function in place of [tex]\( x \)[/tex].
Here’s how we do it step by step:
1. Start with the given function:
[tex]\( f(x) = x^3 - 2x^2 + 7x - 5 \)[/tex].
2. Substitute [tex]\(-3\)[/tex] for [tex]\( x \)[/tex]:
[tex]\( f(-3) = (-3)^3 - 2(-3)^2 + 7(-3) - 5 \)[/tex].
3. Calculate each term:
- [tex]\( (-3)^3 = -27 \)[/tex]
- [tex]\( -2(-3)^2 = -2 \cdot 9 = -18 \)[/tex]
- [tex]\( 7(-3) = -21 \)[/tex]
- The constant term is [tex]\(-5\)[/tex].
4. Now, combine all the terms:
[tex]\( f(-3) = -27 - 18 - 21 - 5 \)[/tex].
5. Simplify by adding them together:
[tex]\(-27 - 18 = -45\)[/tex]
[tex]\(-45 - 21 = -66\)[/tex]
[tex]\(-66 - 5 = -71\)[/tex]
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\(-71\)[/tex].
The correct answer is (A) -71.
Here’s how we do it step by step:
1. Start with the given function:
[tex]\( f(x) = x^3 - 2x^2 + 7x - 5 \)[/tex].
2. Substitute [tex]\(-3\)[/tex] for [tex]\( x \)[/tex]:
[tex]\( f(-3) = (-3)^3 - 2(-3)^2 + 7(-3) - 5 \)[/tex].
3. Calculate each term:
- [tex]\( (-3)^3 = -27 \)[/tex]
- [tex]\( -2(-3)^2 = -2 \cdot 9 = -18 \)[/tex]
- [tex]\( 7(-3) = -21 \)[/tex]
- The constant term is [tex]\(-5\)[/tex].
4. Now, combine all the terms:
[tex]\( f(-3) = -27 - 18 - 21 - 5 \)[/tex].
5. Simplify by adding them together:
[tex]\(-27 - 18 = -45\)[/tex]
[tex]\(-45 - 21 = -66\)[/tex]
[tex]\(-66 - 5 = -71\)[/tex]
Therefore, the value of [tex]\( f(-3) \)[/tex] is [tex]\(-71\)[/tex].
The correct answer is (A) -71.
