Expressing a given function

Question

Express the given function h(x)=√x³-2 as the composition of two functions f and g so that h(x) = (f º g)(x). In other words, find two functions f and g which decompose h(x).

 

 (that radical applies to the entirety x³-2)

Answer 1

Let g(x) = x³ - 2  (the "inside" function)

 

      f(x) = √x      (the "outside" function)

 

Then, h(x) = (f ο g)(x) = f(g(x)) = f(x³ - 2) = √(x³ - 2)

Answer 2

Given   h(x) = √(x³ - 2)

 

(f ° g)(x) = f(g(x))

 

 

f(x) is the outer function.  The outer function is a radical term.  f(x) = √x

 

g(x) is the inner function.  The inner function is the term that is inside the radical.  g(x) = x³ - 2