Write the given function as the composite of two functions, neither of which is the identity function f(x)=x f(x)=\sqrt[3]{x^(2)+2 }

Question

Write the given function as the composite of two functions, neither of which is the identity function f(x)=x

f(x)=
`\sqrt[3]{x^(2)+2 }`

Answer 1

composite functions are

`f(x)=\sqrt[3]{x}`

`g(x)=x^2+2`

Explanation:

We are given

`f(x)=\sqrt[3]{x^2+2}`

Since, f(x) is composite function

`f(x)=f(g(x))`

Let's assume

`g(x)=x^2+2`

we can replace x^2+2 as g(x)

`f(g(x)))=\sqrt[3]{g(x)}`

now, we can replace g(x) as x

`f(x)=\sqrt[3]{x}`

so, composite functions are

`f(x)=\sqrt[3]{x}`

`g(x)=x^2+2`