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Question 3 (5 points)

Given [tex]\( f(x) = \left(\frac{1}{4}\right)^{-x} \)[/tex], evaluate [tex]\( f(2) \)[/tex], [tex]\( f(1) \)[/tex], and [tex]\( f(-2) \)[/tex].

A. [tex]\( 16, \frac{1}{4}, \frac{1}{16} \)[/tex]
B. [tex]\( 16, 4, \frac{1}{16} \)[/tex]
C. [tex]\( 16, 4, 16 \)[/tex]
D. [tex]\( \frac{1}{16}, 4, 16 \)[/tex]



Answer :

GinnyAnswer
To solve for the values of [tex]\( f(x) \)[/tex] for the given function [tex]\( f(x) = \left(\frac{1}{4}\right)^{-x} \)[/tex]:

1. Evaluate [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = \left(\frac{1}{4}\right)^{-2} \][/tex]
[tex]\[ \left(\frac{1}{4}\right)^{-2} = 4^2 = 16 \][/tex]
So, [tex]\( f(2) = 16 \)[/tex].

2. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[ f(1) = \left(\frac{1}{4}\right)^{-1} \][/tex]
[tex]\[ \left(\frac{1}{4}\right)^{-1} = 4^1 = 4 \][/tex]
So, [tex]\( f(1) = 4 \)[/tex].

3. Evaluate [tex]\( f(2) \)[/tex] again:
[tex]\[ f(2) = \left(\frac{1}{4}\right)^{-2} \][/tex]
As computed earlier,
[tex]\[ \left(\frac{1}{4}\right)^{-2} = 16 \][/tex]
So, [tex]\( f(2) = 16 \)[/tex] again.

After evaluating these expressions, we find that:

- [tex]\( f(2) = 16 \)[/tex]
- [tex]\( f(1) = 4 \)[/tex]
- [tex]\( f(2) = 16 \)[/tex]

Thus, the correct choice from the given multiple-choice options is:

[tex]\[ \boxed{16, 4, 16} \][/tex]