Question

Find the first 3 iterates of the function f(x)=-2x + 3 when x0=0

Answer 1

The first three iterates of the function f(x)=-2x + 3 starting with x0=0 are f1(x)=3, f2(x)=-3, and f3(x)=9.

Step-by-step explanation:

To find the first three iterates of the function f(x)=-2x + 3 starting with x0=0, we will apply the function to the starting value and then use each result as the input for the next step.

1. Apply f to x0: f1(x) = f(0) = -2(0) + 3 = 3.
2. Apply f to f1(x): f2(x) = f(3) = -2(3) + 3 = -6 + 3 = -3.
3. Apply f to f2(x): f3(x) = f(-3) = -2(-3) + 3 = 6 + 3 = 9.

Therefore, the first three iterates of the function when starting with x0=0 are 3, -3, and 9.