Question

F(x) = 1/x ,f(f(f(f(f(f(x))))))=??

f(x) = 1/x ,f(f(f(f(f(f(x))))))=??

Answer 1

`f` is its own inverse, so an even number of them composed, six here, gets us back where we started:

`f(f(f(f(f(f(x)))))) = x`

Explanation:

One application of `f` gives the reciprocal:

`f(x) = 1/x`

Two gives us the reciprocal of the reciprocal, which is `x`

`f(f(x)) = f(1/x) = 1/(1/x) = x`

Three applications give us `1/x`:

`f(f(f(x)))=f(x) = 1/x`

We see four applications gives us `x`, five gives us `1/x`, etc. An even number gives us `x` and an odd number `1/x`.