Answer:To find the value of f(4) using the given information, we can work through the recursive relationship provided: f(n+1) = f(n)^2 + 1.
We know that f(1) = 4. Let's find the values of f(2), f(3), and finally f(4) by substituting the previous values into the equation.
1. Substitute n = 1 into the equation:
f(2) = f(1)^2 + 1 = 4^2 + 1 = 16 + 1 = 17.
2. Substitute n = 2 into the equation:
f(3) = f(2)^2 + 1 = 17^2 + 1 = 289 + 1 = 290.
3. Substitute n = 3 into the equation:
f(4) = f(3)^2 + 1 = 290^2 + 1 = 84100 + 1 = 84101.
Therefore, the value of f(4) is 84101, based on the recursive relationship f(n+1) = f(n)^2 + 1 and the initial condition f(1) = 4.
Step-by-step explanation:
