Find f(f(x))

[harpazo]

 

[HallsofIvy]

Yes, that is correct.

 

[topsquark]

Actually, I'd changet the first few lines. x is not, in general, equal to f(x) so you can't say x = f(x) and substitute.

This is all a "language" problem. I'd do the following:
f(x) = 1/x

Let f(x) = y. Then f(f(x)) = f(y) = 1/y and go from there.

Or you could skip the problem entirely and do f(x) = 1/x implies f(f(x)) = f(1/x) = 1/(1/x).

-Dan

 

[harpazo]

Actually, I'd changet the first few lines. x is not, in general, equal to f(x) so you can't say x = f(x) and substitute.

This is all a "language" problem. I'd do the following:
f(x) = 1/x

Let f(x) = y. Then f(f(x)) = f(y) = 1/y and go from there.

Or you could skip the problem entirely and do f(x) = 1/x implies f(f(x)) = f(1/x) = 1/(1/x).

-Dan

Good to know other methods.