To find the values of the function [tex]\( f(x) = 9^{-x} \)[/tex] at specific points, we will substitute the values of [tex]\( x \)[/tex] into the function and calculate.
1. Calculating [tex]\( f(1) \)[/tex]:
[tex]\[ f(1) = 9^{-1} \][/tex]
The expression [tex]\( 9^{-1} \)[/tex] is equivalent to the reciprocal of 9:
[tex]\[ 9^{-1} = \frac{1}{9} \][/tex]
Thus,
[tex]\[ f(1) = \frac{1}{9} \approx 0.1111111111111111 \][/tex]
2. Calculating [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 9^{-2} \][/tex]
The expression [tex]\( 9^{-2} \)[/tex] is equivalent to the reciprocal of [tex]\( 9^2 \)[/tex], since negative exponents indicate reciprocals:
[tex]\[ 9^{-2} = \frac{1}{9^2} = \frac{1}{81} \][/tex]
Thus,
[tex]\[ f(2) = \frac{1}{81} \approx 0.012345679012345678 \][/tex]
So, the calculated function values are:
[tex]\[
\begin{array}{l}
f(1)=0.1111111111111111 \\
f(2)=0.012345679012345678
\end{array}
\][/tex]
