To solve the problem and find the value of [tex]\( f(-5) \)[/tex] for the function [tex]\( f(x) = x^3 - 2x^2 + 3x - 5 \)[/tex], we need to evaluate the function at [tex]\( x = -5 \)[/tex].
Let's break this down step-by-step:
1. Substitute [tex]\( x = -5 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-5) = (-5)^3 - 2(-5)^2 + 3(-5) - 5
\][/tex]
2. Calculate each term individually:
[tex]\[
(-5)^3 = -125
\][/tex]
[tex]\[
-2(-5)^2 = -2 \cdot 25 = -50
\][/tex]
[tex]\[
3(-5) = -15
\][/tex]
3. Now, combine these results and simplify:
[tex]\[
f(-5) = -125 - 50 - 15 - 5
\][/tex]
4. Add these values together:
[tex]\[
-125 - 50 = -175
\][/tex]
[tex]\[
-175 - 15 = -190
\][/tex]
[tex]\[
-190 - 5 = -195
\][/tex]
Thus, the value of [tex]\( f(-5) \)[/tex] is [tex]\( -195 \)[/tex].
