Find two functions f and g such that (f ∘ g)(x) = h(x).

Question

h(x) = 1 over x + 1
(f(x), g(x)) = ?

Answer 1

I assume you mean

 

h(x) = 1/(x + 1)

 

(Please group things in parentheses!)

 

Consider:

 

g(x) = x + 1

f(x) = 1/x

 

Then 

 

f(g(x)) = 1/g(x) = 1/(x + 1)

Answer 2

g(x) = x + 1

f(x) = 1 / x