Answer:
The function is [tex]f(x)=4(x)^2[/tex]
Step-by-step explanation:
Given : If [tex]f(g(x))= 4(x^6 + 9)^2[/tex] and [tex]g(x)=x^6+9[/tex]
To find : The function f(x) ?
Solution :
[tex]f(g(x))=(fog)(x)[/tex] where the function g is inside of the function f.
We have given,
[tex]f(g(x))= 4(x^6 + 9)^2[/tex]
The function [tex]g(x)=x^6+9[/tex]
Substitute in equation,
[tex]f(g(x))= 4(g(x))^2[/tex]
We know that g(x) is placed over x in the function,
[tex]f(x)= 4(x)^2[/tex]
Therefore, The function is [tex]f(x)=4(x)^2[/tex]
