Given the functions f, of, x, equals, x, to the power 5f(x)=x

Question

5
and g, of, x, equals, 4, dot, 3, to the power xg(x)=4⋅3
x
, which of the following statements is true?
Answer
Multiple Choice Answers
f, of, 2, equals, g, of, 2f(2)=g(2)
f, of, 2, is greater than, g, of, 2f(2)>g(2)
f, of, 2, is less than, g, of, 2f(2)<g(2)

Answer 1

To determine which statement is true, we need to evaluate both functions \(f\) and \(g\) at \(x = 2\).

1. Calculating \(f(2)\): \[ f(x) = x^5 \] Therefore, \[ f(2) = 2^5 = 32. \]

2. Calculating \(g(2)\): \[ g(x) = 4 \cdot 3^x \] Therefore, \[ g(2) = 4 \cdot 3^2 = 4 \cdot 9 = 36. \]

Now we have:

• \( f(2) = 32 \)
• \( g(2) = 36 \)

Now we can compare these values:

• Since \(32 < 36\), we conclude that: \[ f(2) < g(2). \]

Thus, the correct statement is:

\[ \text{f(2) is less than g(2): } f(2) < g(2). \]

So the correct answer is: \( f(2) < g(2) \).