Questions: Use the table below to fill in the missing values. x f(x) ------ 0 2 1 5 2 3 3 8 4 4 5 6 6 0 7 9 8 7 9 1 f(7)= if f(x)=7, then x= f^(-1)(9)= if f^(-1)(x)=8, then x=

Transcript text: Use the table below to fill in the missing values. \begin{tabular}{|r|r|} \hline$x$ & $f(x)$ \\ \hline 0 & 2 \\ \hline 1 & 5 \\ \hline 2 & 3 \\ \hline 3 & 8 \\ \hline 4 & 4 \\ \hline 5 & 6 \\ \hline 6 & 0 \\ \hline 7 & 9 \\ \hline 8 & 7 \\ \hline 9 & 1 \\ \hline \end{tabular} \[ f(7)= \] $\square$ if $f(x)=7$, then $x=$ $\square$ \[ f^{-1}(9)= \] $\square$ if $f^{-1}(x)=8$, then $x=$ $\square$

Solution

Solution Steps

To solve the given problems, we need to interpret the table as a function mapping from $ x $ to $ f(x) $. For each question, we will look up the corresponding value in the table or find the inverse mapping where necessary.

To find $ f(7) $, we look up the value of $ f(x) $ when $ x = 7 $.
To find $ x $ such that $ f(x) = 7 $, we search for the $ x $ value in the table where $ f(x) $ equals 7.
To find $ f^{-1}(9) $, we determine the $ x $ value such that $ f(x) = 9 $.

Step 1: Determine $ f(7) $

To find $ f(7) $, we look up the value of $ f(x) $ when $ x = 7 $ in the table. According to the table, $ f(7) = 9 $.

Step 2: Find $ x $ such that $ f(x) = 7 $

We need to find the value of $ x $ for which $ f(x) = 7 $. By examining the table, we see that when $ x = 8 $, $ f(x) = 7 $.

Step 3: Determine $ f^{-1}(9) $

To find $ f^{-1}(9) $, we need to determine the value of $ x $ such that $ f(x) = 9 $. From the table, we see that when $ x = 7 $, $ f(x) = 9 $.