Question

given the functions $f(x) = 4x$ and $g(x) = 6 \cdot 2^x$, which of the following statements is true?
answer
$\circ$ $f(2) < g(2)$ $\circ$ $f(2) = g(2)$ $\circ$ $f(2) > g(2)$

Explanation:

Step1: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) = 4x \).
\( f(2) = 4\times2 = 8 \)

Step2: Calculate \( g(2) \)

Substitute \( x = 2 \) into \( g(x) = 6\cdot2^{x} \).
\( g(2) = 6\times2^{2} = 6\times4 = 24 \)

Step3: Compare \( f(2) \) and \( g(2) \)

Since \( 8 < 24 \), we have \( f(2) < g(2) \).

Answer:

\( f(2) < g(2) \) (the option with \( f(2) < g(2) \))