Question

use the table below to fill in the missing values.

$x$	$f(x)$
1	2
2	4
3	5
4	3
5	6
6	8
7	7
8	9
9	0

$f(1) = \square$

if $f(x) = 6$, then $x = \square$

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

if $f^{-1}(x) = 5$, then $x = \square$

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Explanation:

Step1: Find \( f(1) \)

Look at the table where \( x = 1 \). The corresponding \( f(x) \) value is 2.

Step2: Find \( x \) when \( f(x) = 6 \)

Search the table for \( f(x) = 6 \). The \( x \) value corresponding to \( f(x) = 6 \) is 5.

Step3: Find \( f^{-1}(2) \)

The inverse function \( f^{-1}(y) \) gives the \( x \) such that \( f(x) = y \). So we look for \( f(x) = 2 \), and the corresponding \( x \) is 1.

Step4: Find \( x \) when \( f^{-1}(x) = 5 \)

\( f^{-1}(x) = 5 \) means \( f(5) = x \). From the table, when \( x = 5 \), \( f(x) = 6 \), so \( x = 6 \).

Answer:

\( f(1) = 2 \)
if \( f(x) = 6 \), then \( x = 5 \)
\( f^{-1}(2) = 1 \)
if \( f^{-1}(x) = 5 \), then \( x = 6 \)