Question

Given the functions f, of, x, equals, 4, x, to the power 4f(x)=4x
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:
\[
\boxed{f(6) > g(6)}.
\]