Question

If f(g(x)) = 4(x^6 + 9)^2 and g(x)=x^6+9, find f(x). f(x) help (formulas)

Answer 1

The function is
`f(x)=4(x)^2`

Explanation:

Given : If
`f(g(x))= 4(x^6 + 9)^2` and
`g(x)=x^6+9`

To find : The function f(x) ?

Solution :

`f(g(x))=(fog)(x)` where the function g is inside of the function f.

We have given,

`f(g(x))= 4(x^6 + 9)^2`

The function
`g(x)=x^6+9`

Substitute in equation,

`f(g(x))= 4(g(x))^2`

We know that g(x) is placed over x in the function,

`f(x)= 4(x)^2`

Therefore, The function is
`f(x)=4(x)^2`