What is the value of g(f(2x)) if f(x) is defined as 4x^2 and g(x) is defined as 5x?

To determine the value of g(f(2x)), we start with the definitions of the functions given:

• Function f(x) = 4x²
• Function g(x) = 5x

We will first calculate f(2x):

f(2x) = 4(2x)2
     = 4(4x2)
     = 16x2

Next, we take this result and substitute it into the function g(x):

g(f(2x)) = g(16x2)
           = 5(16x2)
           = 80x2

Therefore, the final result is:

g(f(2x)) = 80x²