Given function f(x)=1/1+x find: a)(f o f)(x) b)For what values ​​of x does the subsection make sense a)

Question

Given function f(x)=1/1+x find:

a)(f o f)(x)

b)For what values ​​of x does the subsection make sense a)

Answer 1

f°f(x) = 1 / (1 + 1/(1+x)) = 1 / ((1+ x) + 1)/(1+x)) = (1+x) / (2+x)

This composite function's domain is all x ≠ - 1 , - 2.

The first restriction comes from the original function, the 2nd comes from the fact that f(-2) = -1.