for h (x) = ^3 Radical (X^2 + 9) define two functions f(x) and g(x)...

Question

for h(x) = ^3 Radical (X^2 + 9) define two functions f(x) and g(x) such that h is the composite of f and g; in other words decompose h into f and g so that h(x)=f(g(x))

 

-h(x) = (x^2 + 9) is under the radical and the radical is raised (in the front) to the 3rd power

Answer 1

I assume you mean

 

h(x) = [√(x² + 9)]³

 

There is more than one way to get h(x) from composing 2 functions.  Here is one:

 

g(x) = √(x² + 9)

 

Let f(x) = x³

 

f(g(x)) = [√(x² + 9)]³

 

Here is another:

 

You can express h(x) as

 

h(x) = (x² + 9)^3/2 = √[(x² + 9)³]

 

g(x) = (x² + 9)³

 

f(x) = √x

 

f(g(x)) = √[(x² + 9)³]

 

 

Answer 2

f(x) = ³√x

g(x) = x² + 9