Given:
The composition of functions is G(F(y)).
To find:
The independent variable of G(F(y)).
Solution:
Independent variable is the variable whose value independent from other variable. It means the value of independent variables is not depend on the other variable.
We know that G(F(y)) can be written as

Here, the value of function G depends on F(y) and the value of F(y) depend on variable y. But value of y does not depend on any variable. So, y is the independent variable of G(F(y)).
Therefore, the correct option is C.
The third picture3rd graph
Answer:

Step-by-step explanation:
Given
![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7B1%7D%7B64%7De%5E%7B-4x%7D%5BAx%5E2%20%2B%20Bx%20%2B%20E%5DC)
Required
Find 
We have:
![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7B1%7D%7B64%7De%5E%7B-4x%7D%5BAx%5E2%20%2B%20Bx%20%2B%20E%5DC)
Using integration by parts

Where
and 
Solve for du (differentiate u)

Solve for v (integrate dv)

So, we have:




-----------------------------------------------------------------------
Solving

Integration by parts
---- 
---------- 
So:



So, we have:

![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}]](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7Bx%5E2%7D%7B4%7De%5E%7B-4x%7D%20%2B%5Cfrac%7B1%7D%7B2%7D%20%5B%20-%5Cfrac%7Bx%7D%7B4%7De%5E%7B-4x%7D%20%20-%5Cfrac%7B1%7D%7B4%7De%5E%7B-4x%7D%5D)
Open bracket

Factor out 
![\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20%5B-%5Cfrac%7Bx%5E2%7D%7B4%7D%20-%5Cfrac%7Bx%7D%7B8%7D%20-%5Cfrac%7B1%7D%7B8%7D%5De%5E%7B-4x%7D)
Rewrite as:
![\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20%5B-%5Cfrac%7B1%7D%7B4%7Dx%5E2%20-%5Cfrac%7B1%7D%7B8%7Dx%20-%5Cfrac%7B1%7D%7B8%7D%5De%5E%7B-4x%7D)
Recall that:
![\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20-%5Cfrac%7B1%7D%7B64%7De%5E%7B-4x%7D%5BAx%5E2%20%2B%20Bx%20%2B%20E%5DC)
![\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7Bx%5E2%5Ccdot%20e%5E%7B-4x%7D%7D%20%5C%2C%20dx%20%20%3D%20%5B-%5Cfrac%7B1%7D%7B64%7DAx%5E2%20-%5Cfrac%7B1%7D%7B64%7D%20Bx%20-%5Cfrac%7B1%7D%7B64%7D%20E%5DCe%5E%7B-4x%7D)
By comparison:



Solve A, B and C

Divide by 

Multiply by 64



Divide by 

Multiply by 64



Multiply by -64


So:


Answer:

Step-by-step explanation:
Q) 5 × (4/9) = ?
→ (5 × 4)/9
→ 20/9

G should be the correct answer
Hope this helps!