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:

$$f(2)=8\text{and}g(2)=24$$

Since $8<24$, we can conclude that:

$$f(2)<g(2)$$

Therefore, the correct answer is:

$f(2)<g(2)$.