Final answer:
By substituting x=4 into the function f(x) = 5x^4 - 3x^3 + 6x^2 - x + 12 and calculating each term, we find that f(4) equals 1192.
Step-by-step explanation:
To find f(4) for the function f(x) = 5x^4 - 3x^3 + 6x^2 - x + 12, we need to substitute x = 4 into the equation and simplify:
First, calculate the term with the highest exponent: 5 * 4^4 which is 5 * 256 giving 1280.
Then, calculate the next term: -3 * 4^3 which is -3 * 64 giving -192.
Move on to the quadratic term: 6 * 4^2 which is 6 * 16 giving 96.
Next, calculate the linear term: -1 * 4 giving -4.
Finally, add the constant term: 12.
Add all these results together: 1280 - 192 + 96 - 4 + 12 to get f(4).
Therefore, f(4) = 1280 - 192 + 96 - 4 + 12 = 1192.
The value of f(4) is 1192.