Final answer:
The value of f(3) is 13, as it is determined by evaluating the given linearization L(x)=4x+1 at x=3.
Step-by-step explanation:
The student is asking for the value of f(3) given that the linearization of f(x) at a=3 is L(x)=4x+1. The linearization of a function at a point is the best linear approximation of the function near that point. So, the value of the function at a=3, which is f(3), will be the same as the linear approximation at that point. Therefore, to find f(3), we simply need to evaluate the linearization L(x) at x=3.
f(3) = L(3) = 4(3) + 1 = 12 + 1 = 13.
Thus, f(3) equals 13.