Find the first three iterates x1,x2,x3 of f(x)=2x-5 for an initial value of x0=3.
x1=f(x0)
=f(1)
=2(1)-5
=-3
2(-3)-5
-6-5
-11
2(-11)-5
-22-5
-27
the first three iterates are: -3,-11,-27
To find the first three iterates of the function f(x) = 2x-5 with an initial value of x0=3, you can use repeated substitution:
1. Start with the initial value, x0=3.
2. Substitute x0 into the function f(x) = 2x-5:
x1 = f(x0) = 2(3)-5 = -3
3. Substitute x1 into the function f(x) = 2x-5:
x2 = f(x1) = 2(-3)-5 = -11
4. Substitute x2 into the function f(x) = 2x-5:
x3 = f(x2) = 2(-11)-5 = -27
Therefore, the first three iterates of the function f(x) = 2x-5 with an initial value of x0=3 are -3, -11, and -27.