Answer :
To evaluate the function [tex]\( f(x) = -x^6 + 7x^5 - x^4 + 2x^3 + 9x^2 - 8x - 2 \)[/tex] at a specific value of [tex]\( x \)[/tex], such as [tex]\( x = 2 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = -(2)^6 + 7(2)^5 - (2)^4 + 2(2)^3 + 9(2)^2 - 8(2) - 2
\][/tex]
2. Calculate each term separately:
- [tex]\( -(2)^6 = -64 \)[/tex]
- [tex]\( 7(2)^5 = 224 \)[/tex]
- [tex]\( -(2)^4 = -16 \)[/tex]
- [tex]\( 2(2)^3 = 16 \)[/tex]
- [tex]\( 9(2)^2 = 36 \)[/tex]
- [tex]\( -8(2) = -16 \)[/tex]
- The constant term is [tex]\(-2\)[/tex].
3. Combine all the calculated values:
[tex]\[
f(2) = -64 + 224 - 16 + 16 + 36 - 16 - 2
\][/tex]
4. Add and subtract the values step-by-step:
[tex]\[
= (-64 + 224) + (-16 + 16) + (36 - 16) - 2
\][/tex]
Simplifying further:
[tex]\[
= 160 + 0 + 20 - 2
\][/tex]
[tex]\[
= 178
\][/tex]
Therefore, the value of [tex]\( f(2) \)[/tex] is 178.
1. Substitute [tex]\( x = 2 \)[/tex] into the function:
[tex]\[
f(2) = -(2)^6 + 7(2)^5 - (2)^4 + 2(2)^3 + 9(2)^2 - 8(2) - 2
\][/tex]
2. Calculate each term separately:
- [tex]\( -(2)^6 = -64 \)[/tex]
- [tex]\( 7(2)^5 = 224 \)[/tex]
- [tex]\( -(2)^4 = -16 \)[/tex]
- [tex]\( 2(2)^3 = 16 \)[/tex]
- [tex]\( 9(2)^2 = 36 \)[/tex]
- [tex]\( -8(2) = -16 \)[/tex]
- The constant term is [tex]\(-2\)[/tex].
3. Combine all the calculated values:
[tex]\[
f(2) = -64 + 224 - 16 + 16 + 36 - 16 - 2
\][/tex]
4. Add and subtract the values step-by-step:
[tex]\[
= (-64 + 224) + (-16 + 16) + (36 - 16) - 2
\][/tex]
Simplifying further:
[tex]\[
= 160 + 0 + 20 - 2
\][/tex]
[tex]\[
= 178
\][/tex]
Therefore, the value of [tex]\( f(2) \)[/tex] is 178.
