Question

use the table below to fill in the missing values.

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

$f(4)=$
if $f(x)=9$, then $x=$
$f^{-1}(1)=$
if $f^{-1}(x)=1$, then $x=$
question help: video

Explanation:

Step1: Find f(4)

Look for x = 4 in the table. When x = 4, f(x)=1.

Step2: Find x when f(x) = 9

Look for f(x)=9 in the table. When f(x) = 9, x = 1.

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

The inverse function \(f^{-1}(y)\) gives the x - value such that f(x)=y. When y = 1, from the table x = 4, so \(f^{-1}(1)=4\).

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

If \(f^{-1}(x)=1\), then f(1)=x. From the table, f(1)=9, so x = 9.

Answer:

f(4) = 1
if f(x) = 9, then x = 1
\(f^{-1}(1)=4\)
if \(f^{-1}(x)=1\), then x = 9