Answer :
To find [tex]\( f(-3) \)[/tex] for the function [tex]\( f(x) = 3x^4 - 2x^3 + 7x^2 + 5x - 23 \)[/tex], follow these steps:
1. Substitute [tex]\( x = -3 \)[/tex] into the function:
Start with the function:
[tex]\[
f(x) = 3x^4 - 2x^3 + 7x^2 + 5x - 23
\][/tex]
Replace [tex]\( x \)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
f(-3) = 3(-3)^4 - 2(-3)^3 + 7(-3)^2 + 5(-3) - 23
\][/tex]
2. Calculate each term separately:
- Calculate [tex]\( (-3)^4 \)[/tex]:
[tex]\[
(-3)^4 = 81
\][/tex]
Multiply by 3:
[tex]\[
3 \times 81 = 243
\][/tex]
- Calculate [tex]\( (-3)^3 \)[/tex]:
[tex]\[
(-3)^3 = -27
\][/tex]
Multiply by -2:
[tex]\[
-2 \times (-27) = 54
\][/tex]
- Calculate [tex]\( (-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
Multiply by 7:
[tex]\[
7 \times 9 = 63
\][/tex]
- Calculate [tex]\( 5 \times (-3) \)[/tex]:
[tex]\[
5 \times (-3) = -15
\][/tex]
- The constant [tex]\(-23\)[/tex] remains as it is.
3. Add all the results together:
[tex]\[
f(-3) = 243 + 54 + 63 - 15 - 23
\][/tex]
Proceed with the addition and subtraction:
[tex]\[
243 + 54 = 297
\][/tex]
[tex]\[
297 + 63 = 360
\][/tex]
[tex]\[
360 - 15 = 345
\][/tex]
[tex]\[
345 - 23 = 322
\][/tex]
Therefore, [tex]\( f(-3) = 322 \)[/tex].
1. Substitute [tex]\( x = -3 \)[/tex] into the function:
Start with the function:
[tex]\[
f(x) = 3x^4 - 2x^3 + 7x^2 + 5x - 23
\][/tex]
Replace [tex]\( x \)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
f(-3) = 3(-3)^4 - 2(-3)^3 + 7(-3)^2 + 5(-3) - 23
\][/tex]
2. Calculate each term separately:
- Calculate [tex]\( (-3)^4 \)[/tex]:
[tex]\[
(-3)^4 = 81
\][/tex]
Multiply by 3:
[tex]\[
3 \times 81 = 243
\][/tex]
- Calculate [tex]\( (-3)^3 \)[/tex]:
[tex]\[
(-3)^3 = -27
\][/tex]
Multiply by -2:
[tex]\[
-2 \times (-27) = 54
\][/tex]
- Calculate [tex]\( (-3)^2 \)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
Multiply by 7:
[tex]\[
7 \times 9 = 63
\][/tex]
- Calculate [tex]\( 5 \times (-3) \)[/tex]:
[tex]\[
5 \times (-3) = -15
\][/tex]
- The constant [tex]\(-23\)[/tex] remains as it is.
3. Add all the results together:
[tex]\[
f(-3) = 243 + 54 + 63 - 15 - 23
\][/tex]
Proceed with the addition and subtraction:
[tex]\[
243 + 54 = 297
\][/tex]
[tex]\[
297 + 63 = 360
\][/tex]
[tex]\[
360 - 15 = 345
\][/tex]
[tex]\[
345 - 23 = 322
\][/tex]
Therefore, [tex]\( f(-3) = 322 \)[/tex].
