Find the first three iterates of the function f(x)=x^2-2, if the intial value is -2.
z(0)=-2
z(1)=(-2)^2-2 or 4-2=2
z(2)=(2)^2-2 or 4-2=2
z(3)=(2)^2-2 or 4-2=2
Answer: z(1)=2, z(2)=2, z(3)=2
correct.
Thanks
To find the first three iterates of the function f(x)=x^2-2, starting with an initial value of -2, you can follow these steps:
1. Start with the initial value z(0) = -2.
2. Substitute -2 into the function f(x) = x^2 - 2 to find the first iterate: z(1) = (-2)^2 - 2 = 4 - 2 = 2.
3. Substitute 2 into the function f(x) = x^2 - 2 to find the second iterate: z(2) = (2)^2 - 2 = 4 - 2 = 2.
4. Substitute 2 into the function f(x) = x^2 - 2 to find the third iterate: z(3) = (2)^2 - 2 = 4 - 2 = 2.
So, the first three iterates of the function f(x) = x^2 - 2, starting with an initial value of -2, are z(1) = 2, z(2) = 2, and z(3) = 2.