Question

2
type the correct answer in each box.
consider the table modeling function $f$.
$x$ -2 -1 0 1 2
$f(x)$ -28 -9 -2 -1 0
complete the table modeling the inverse of function $f$.
$x$ $quad$ $quad$ $quad$ -1 0
$f^{-1}(x)$ -2 $quad$ 0 $quad$ $quad$

Explanation:

Step1: Recall inverse function definition

For a function $f$, if $f(a)=b$, then $f^{-1}(b)=a$.

Step2: Match values from original table

• When $f^{-1}(x)=-2$, find $x$ where $f(-2)=-28$, so $x=-28$.
• When $x=-9$, find $a$ where $f(a)=-9$, so $f^{-1}(-9)=-1$.
• When $f^{-1}(x)=0$, find $x$ where $f(0)=-2$, so $x=-2$.
• When $x=-1$, find $a$ where $f(a)=-1$, so $f^{-1}(-1)=1$.
• When $x=0$, find $a$ where $f(a)=0$, so $f^{-1}(0)=2$.

Answer:

The completed table has the following filled values (in order of empty boxes):
Top row (x values): $-28$, $-9$, $-2$
Bottom row ($f^{-1}(x)$ values): $-1$, $1$, $2$

Full completed table:

$x$	$-28$	$-9$	$-2$	$-1$	$0$