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

Question

4
and g, of, x, equals, 4, to the power xg(x)=4
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, of, 6, is less than, g, of, 6f(6)<g(6)
f, of, 6, equals, g, of, 6f(6)=g(6)
f, of, 6, is greater than, g, of, 6f(6)>g(6)

Answer 1

To evaluate the functions \( f(x) \) and \( g(x) \) at \( x = 6 \), we first need to explicitly define both functions:

• \( f(x) = 4x^4 \)
• \( g(x) = 4^x \)

Now we will calculate \( f(6) \) and \( g(6) \):

1. Calculating \( f(6) \): \[ f(6) = 4(6^4) \] \[ 6^4 = 1296, \quad \text{so} \quad f(6) = 4 \times 1296 = 5184. \]

2. Calculating \( g(6) \): \[ g(6) = 4^6 \] \[ 4^6 = (4^2)^3 = 16^3 = 4096. \]

Now we need to compare \( f(6) \) and \( g(6) \):

• \( f(6) = 5184 \)
• \( g(6) = 4096 \)

Now we can see that: \[ f(6) = 5184 > g(6) = 4096. \]

Thus, the statement that is true is: \[ \boxed{f(6) > g(6)}. \]