# Example of function decomposition .Give an example of function decomposition .

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### 1 Answer

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)