Question

Express the giving function each as a composition of two functions F and g so that

Answer 1

Given the function:

`h(x)=\sqrt[4]{x^3-1}`

We will find the functions f(x) and g(x) so that (fog)(x) = h(x)

So, there are many solutions for the question, we will write one of them

The function h(x) will be when the substitution with g(x) into the function f(x)

so, the function will be as follows:

`\begin{gathered} f(x)=^4\sqrt[]{x} \\ g(x)=x^3-1 \end{gathered}`

Note: g(x) must be (x³ - 1) because it is given in the question one of the functions will be equal to it

So, the other function will be f(x)

So, the answer will be:

`f(x)=^4\sqrt[]{x}`