To determine the output of the given function [tex]\( F(x) = -x^3 - 2x^2 + 7x - 10 \)[/tex] for [tex]\( x = 1 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 1 \)[/tex] into the function [tex]\( F(x) \)[/tex]:
[tex]\[
F(1) = - (1)^3 - 2(1)^2 + 7(1) - 10
\][/tex]
2. Calculate each term:
[tex]\[
(1)^3 = 1
\][/tex]
[tex]\[
2(1)^2 = 2
\][/tex]
[tex]\[
7(1) = 7
\][/tex]
3. Substitute these values back into the equation:
[tex]\[
F(1) = -1 - 2 + 7 - 10
\][/tex]
4. Perform the arithmetic operations step by step:
[tex]\[
-1 - 2 = -3
\][/tex]
[tex]\[
-3 + 7 = 4
\][/tex]
[tex]\[
4 - 10 = -6
\][/tex]
Therefore, the output of the function [tex]\( F(x) = -x^3 - 2x^2 + 7x - 10 \)[/tex] for [tex]\( x = 1 \)[/tex] is:
[tex]\[
\boxed{-6}
\][/tex]
