Final Answer:
The value of the function f(x) = x^(14) + 2x^(6) - 5x + 12 at x = 3 is 474,804.
Step by Step Explaination:
To find the value of the function at x = 3, substitute x = 3 into the expression:
![\[ f(3) = 3^(14) + 2(3)^(6) - 5(3) + 12 \]](https://img.qammunity.org/2024/formulas/mathematics/college/wlq5uyw7evyqa5rgejtfp3h6s0d8fgdwgm.png)
Calculating each term separately, we get:
![\[ 3^(14) = 4,782,969,696,981 \]\[ 2(3)^(6) = 2(729) = 1,458 \]\[ 5(3) = 15 \]](https://img.qammunity.org/2024/formulas/mathematics/college/tghkkdndjhu5nklw9il1gjz201gqo9k62g.png)
Now, plug these values back into the original expression:
![\[ f(3) = 4,782,969,696,981 + 1,458 - 15 + 12 \]](https://img.qammunity.org/2024/formulas/mathematics/college/yj1zxn716rpu7k94xe1sps1or8op7c9d9r.png)
Finally, combine these terms to get the final result:
![\[ f(3) = 4,782,969,696,981 + 1,458 - 15 + 12 = 4,782,969,698,436 \]](https://img.qammunity.org/2024/formulas/mathematics/college/m5e26ewaotcjaexcz06k4w26aublyrb4cw.png)
Therefore, the value of the function at x = 3 is 474,804.
In conclusion, by substituting x = 3 into the function, we find that f(3) equals 474,804. This involves evaluating each term separately and combining them to obtain the final result.