f(x) = 1/(1−x) is given. From this we produce two new functions:

Question

g(x) = f(f(x)) and h(x) = f(g(x)).

(a) For which values of x is f(x) undefined?
(b) Find a formula for g(x), and simplify it.
(c) For which values of x is g(x) undefined?
(d) Find a formula for h(x), and simplify it.
(e) For which values of x is h(x) undefined?

(Hint: Be careful, because there is a trap here. If a value of x won’t work for f, then it also won’t work for g, because you need to compute f before you compute g!)

(a)f(x)=1/(1-x) ---> 1-x=0 x=1

(b) g(x) = f(f) = 1/(1-f) = 1/(1-(1/(1-x)) = 1 - 1/x

(d) h(x) = f(g) = 1/(1-g) = 1/(1-(1 - 1/x)) = x

So how will I get the

answer for c and e?

Answer 1

(c) clearly g(x) is undefined for x=0
But, it is also undefined for x=1, because f is undefined there.
g(1) = 1/(1-f(1))

Try that logic for h(x).

Answer 2

life is fun