Answer :

To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = 3x^4 - 2x^3 + 7x^2 + 5x - 23 \)[/tex], we substitute [tex]\( x = 3 \)[/tex] into the function and calculate step by step.

1. Start by calculating each power of 3:
- [tex]\( 3^4 = 81 \)[/tex]
- [tex]\( 3^3 = 27 \)[/tex]
- [tex]\( 3^2 = 9 \)[/tex]

2. Substitute these values into the function:
[tex]\[
f(3) = 3(81) - 2(27) + 7(9) + 5(3) - 23
\][/tex]

3. Perform the multiplications:
- [tex]\( 3 \times 81 = 243 \)[/tex]
- [tex]\( 2 \times 27 = 54 \)[/tex]
- [tex]\( 7 \times 9 = 63 \)[/tex]
- [tex]\( 5 \times 3 = 15 \)[/tex]

4. Substitute these results back into the equation:
[tex]\[
f(3) = 243 - 54 + 63 + 15 - 23
\][/tex]

5. Now, perform the additions and subtractions in sequence:
- [tex]\( 243 - 54 = 189 \)[/tex]
- [tex]\( 189 + 63 = 252 \)[/tex]
- [tex]\( 252 + 15 = 267 \)[/tex]
- [tex]\( 267 - 23 = 244 \)[/tex]

Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 244 \)[/tex].

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