If f(x) = 1/(1 - x), g(x) = x/(1 - x), and h(x) = 1/(1 + x), then f[h(x)] =?

Question

I got ... (1 + x)/x
is this correct?

Answer 1

Yes. Thermo's answer is not correct:

f[h(x)] = f [ 1/(1+x)] = f[p] with p = 1/(1+x)

f[p] = 1/(1-p) = 1/(1-(1/(1+x))) = 1/[(1+x-1)/(1+x)] = (1+x) / x

Answer 2

f(x) = 1/(1 - x) and h(x) = 1/(1 + x)
h(x) = 1/(1 + x). Now change x into 1/(1 - x) according to f(x)
f[h(x)] =1/(1 + {1/(1 - x)}) = (1-x)/2-x).

You found -h{f(x)}

Th

Answer 3

It is correct. ( Why g(x) ? )