Give me an example of function decomposition question.

For instance, we'll take the function h(x)=sqrt(x^2 + 1)
and we'll have to decompose it into simpler functions:

h(x)
= f(g(x))

We can take g(x) = x^2 + 1 and f(x) = sqrt
x

Now, we'll compose f(x) and g(x) and we'll
get:

h(x) =
(f*g)(x)

(f*g)(x) =
f(g(x))

f(g(x)) = sqrt
g(x)

We'll substitute g(x) = x^2 +
1

h(x) = f(g(x)) = sqrt (x^2 +
1)

We also can take as f(x) = sqrt  (x+1)
and g(x) = x^2.

(f*g)(x) =
f(g(x))

We'll substitute  the variable x, from the
expression of f(x), by the expression of g(x).

f(g(x)) =
sqrt [g(x) + 1]

h(x) = f(g(x)) = sqrt (x^2+
1)