Find the first three iterates of the given function for the given initial value.

f(x) = 2/x, x_0 = 1. I know this seems simple but whenever i click the "simple" answer, it's always wrong :/

Question

Find the first three iterates of the given function for the given initial value.

f(x) = 2/x, x_0 = 1. I know this seems simple but whenever i click the "simple" answer, it's always wrong :/

anonymous · Answer

If I rewrite it, is it:
x_2 = 2/(x_1)

rainbow_dash · Answer

how do you figure?

anonymous · Answer

$$f(x)=\frac{2}{x}$$ and $x_0=1$ right?

anonymous · Answer

so $x_1=f(x_0)=f(1)=\frac{2}{1}=2$ for the first one

anonymous · Answer

next one, replace $x$ by $x_1=2$ and get 
$$x_2=f(x_1)=f(2)=\frac{2}{2}=1$$ so $x_2=1$

anonymous · Answer

now that we see we are back were we started from, looks like the patter should be clear, 
$$x_0=1,x_1=2,x_2=1,x_3=2,x_4=1,...$$

anonymous · Answer

*pattern (although "patter" sounds good too)