Express the given function as a composition of 2 simple functions (x^3-x^2+2)^7.
In odrer to express the function into two dsimple fuctions, you need to to:
1. Assume that (x^3 - x^2 + 2)= f(x)
Now, assume g(x) = x^7
by replacing x with f(x) you will get g(f(x)) = [f(x)]^7
but, (x^3-x^2+2)^7 = [f(x)]^7 )= g(f(x)so we can compose the function as follow:
g(f(x)) = (x^3-x^2+2)^7, while f(x)= 9x^3-x^2+2)^7
Let's regard the composed function (x^3-x^2+2)^7 in this way:
- we'll put x^3-x^2+2 as being the function g(x);
- we'll put x^7 as being the function f(x).
The result of composition of f(x) and g(x) is:
(f*g)(x) = f(g(x)) = f(x^3-x^2+2) = (x^3-x^2+2)^7 q.e.d.
To express (x^3-x^2+2)^7 as composition of two functions:
Let us define h(x) = (x+2)^7, g(x) = x^3-x^2.
Therefore, h(g(x)) = (x^3 - x^2 + 2)^7