Question

question
given the functions ( f(x) = 4x^3 ) and ( g(x) = 6^x ), which of the following statements is true?
answer
( circ f(4) < g(4) )
( circ f(4) > g(4) )
( circ f(4) = g(4) )

Explanation:

Step1: Calculate \( f(4) \)

Given \( f(x) = 4x^3 \), substitute \( x = 4 \):
\( f(4) = 4\times(4)^3 = 4\times64 = 256 \)

Step2: Calculate \( g(4) \)

Given \( g(x) = 6^x \), substitute \( x = 4 \):
\( g(4) = 6^4 = 1296 \)

Step3: Compare \( f(4) \) and \( g(4) \)

Since \( 256 < 1296 \), we have \( f(4) < g(4) \).

Answer:

\( f(4) < g(4) \) (the option with this statement)