Find the first three iterates of the function f(x)=x^2-2,if the initial value is -2.
To find the first three iterates of the function f(x) = x^2 - 2, we need to repeatedly apply the function starting with an initial value of -2.
1. Start with the initial value, x0 = -2.
f(x0) = f(-2) = (-2)^2 - 2 = 4 - 2 = 2.
2. Use the result from step 1 as the new input for the function.
f(x1) = f(2) = (2)^2 - 2 = 4 - 2 = 2.
3. Repeat the process using the result from step 2.
f(x2) = f(2) = (2)^2 - 2 = 4 - 2 = 2.
So, the first three iterates of the function f(x) = x^2 - 2, with an initial value of -2, are:
x0 = -2,
x1 = 2,
x2 = 2.
To find the first three iterates of the function f(x) = x^2 - 2, we need to start with an initial value and repeatedly substitute it into the function. In this case, the initial value is -2.
1. Start with the initial value: -2
2. Substitute -2 into the function f(x) = x^2 - 2:
- f(-2) = (-2)^2 - 2
= 4 - 2
= 2
So, the first iterate is 2.
3. Substitute 2 into the function:
- f(2) = (2)^2 - 2
= 4 - 2
= 2
The second iterate is also 2.
4. Substitute 2 into the function again:
- f(2) = (2)^2 - 2
= 4 - 2
= 2
The third iterate is also 2.
Therefore, the first three iterates of the function f(x) = x^2 - 2, with an initial value of -2, are 2, 2, and 2.