Answer :
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]
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]
