Given the functions f, of, x, equals, 4, x, to the power 5f(x)=4x

To determine which of the statements is true, we need to calculate \( f(7) \) and \( g(7) \).

Given:

• \( f(x) = 4x^5 \)
• \( g(x) = 7 \cdot 3^x \)

Now, let's calculate each function at \( x = 7 \).

Calculating \( f(7) \): \[ f(7) = 4 \cdot 7^5 \] Calculating \( 7^5 \): \[ 7^5 = 16807 \] So, \[ f(7) = 4 \cdot 16807 = 67228 \]

Calculating \( g(7) \): \[ g(7) = 7 \cdot 3^7 \] Calculating \( 3^7 \): \[ 3^7 = 2187 \] So, \[ g(7) = 7 \cdot 2187 = 15309 \]

Now we compare \( f(7) \) and \( g(7) \):

• \( f(7) = 67228 \)
• \( g(7) = 15309 \)

Since \( 67228 > 15309 \), we have: \[ f(7) > g(7) \]

Thus, the correct statement is: \[ \boxed{f(7) > g(7)} \]