Question

O GRAPHS AND FUNCTIONSExpressing a function as a composition of two functions

Answer 1

As a composite function can be written as:

$(f\circ g)(x)=f(g(x))$

which means that the function of g(x) will be replaced in all the x in present in f(x).

Then, one of the possibilities that this could happen is if:

$g(x)=6x^2-4$$f(x)=\sqrt[3]{x}$

Because:

$(f\circ g)(x)=f(g(x))=\sqrt[3]{6x^2-4}$

Answer:

$g(x)=6x^2-4$$f(x)=\sqrt[3]{x}$