Question

the function $f(x) = \log_3 x$ is represented in the table.

$x$	$f(x)$
3	1
9	2
27	3

complete the table below for the functions inverse, $f^{-1}(x) = 3^x$.

$x$	$f^{-1}(x)$
1	$\square$
2	$\square$
3	$\square$

Explanation:

Step1: For \( x = 0 \)

We use the function \( f^{-1}(x)=3^{x} \). Substitute \( x = 0 \) into the function: \( 3^{0}=1 \) (since any non - zero number to the power of 0 is 1).

Step2: For \( x = 1 \)

Substitute \( x = 1 \) into \( f^{-1}(x)=3^{x} \). We get \( 3^{1}=3 \).

Step3: For \( x = 2 \)

Substitute \( x = 2 \) into \( f^{-1}(x)=3^{x} \). We have \( 3^{2}=9 \) (because \( 3\times3 = 9 \)).

Step4: For \( x = 3 \)

Substitute \( x = 3 \) into \( f^{-1}(x)=3^{x} \). We obtain \( 3^{3}=27 \) (since \( 3\times3\times3=27 \)).

Answer:

When \( x = 0 \), \( f^{-1}(x)=1 \); when \( x = 1 \), \( f^{-1}(x)=3 \); when \( x = 2 \), \( f^{-1}(x)=9 \); when \( x = 3 \), \( f^{-1}(x)=27 \). So the completed table values (from top to bottom) are 1, 3, 9, 27.