Given the functions f, of, x, equals, 4, xf(x)=4x and g, of, x, equals, 6, dot, 2, to the power xg(x)=6⋅2

Question

x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, of, 2, is less than, g, of, 2f(2)<g(2)
f, of, 2, equals, g, of, 2f(2)=g(2)
f, of, 2, is greater than, g, of, 2f(2)>g(2)

Answer 1

To compare \( f(2) \) and \( g(2) \), we first need to evaluate both functions at \( x = 2 \).

Given the functions:

1. \( f(x) = 4x \)
2. \( g(x) = 6 \cdot 2^x \)

Calculating \( f(2) \):

\[ f(2) = 4 \cdot 2 = 8 \]

Now, calculating \( g(2) \):

\[ g(2) = 6 \cdot 2^2 = 6 \cdot 4 = 24 \]

Now, we can compare:

\[ f(2) = 8 \quad \text{and} \quad g(2) = 24 \]

Since \( 8 < 24 \), we can conclude that:

\[ f(2) < g(2) \]

Therefore, the correct answer is:

\( f(2) < g(2) \).