To find [tex]\( f(2) \)[/tex] and [tex]\( f(-2) \)[/tex] given that [tex]\( f(x) = 4^x \)[/tex], let's evaluate the function at both [tex]\( x = 2 \)[/tex] and [tex]\( x = -2 \)[/tex].
First, we compute [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 4^2 \][/tex]
Calculating [tex]\( 4^2 \)[/tex]:
[tex]\[ 4^2 = 4 \times 4 = 16 \][/tex]
So,
[tex]\[ f(2) = 16 \][/tex]
Next, we compute [tex]\( f(-2) \)[/tex]:
[tex]\[ f(-2) = 4^{-2} \][/tex]
Calculating [tex]\( 4^{-2} \)[/tex]:
[tex]\[ 4^{-2} = \frac{1}{4^2} \][/tex]
And since [tex]\( 4^2 = 16 \)[/tex]:
[tex]\[ 4^{-2} = \frac{1}{16} \][/tex]
So,
[tex]\[ f(-2) = \frac{1}{16} \][/tex]
Therefore, the answers are:
[tex]\[ f(2) = 16 \][/tex]
[tex]\[ f(-2) = \frac{1}{16} \][/tex]
