Question

given the functions $f(x) = 3x^4$ and $g(x) = 9 \cdot 3^x$, which of the following statements is true?
answer
$\circ$ $f(3) < g(3)$ $\circ$ $f(3) > g(3)$ $\circ$ $f(3) = g(3)$

Explanation:

Step1: Calculate \( f(3) \)

Substitute \( x = 3 \) into \( f(x)=3x^{4} \).
\( f(3)=3\times3^{4}=3\times81 = 243 \)

Step2: Calculate \( g(3) \)

Substitute \( x = 3 \) into \( g(x)=9\cdot3^{x} \).
\( g(3)=9\times3^{3}=9\times27 = 243 \)

Step3: Compare \( f(3) \) and \( g(3) \)

Since \( f(3) = 243 \) and \( g(3)=243 \), we have \( f(3)=g(3) \).

Answer:

\( f(3) = g(3) \) (the option with \( f(3) = g(3) \))