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=

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 $x=$ $\square$
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Solution

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Solution Steps

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

  1. To find f(7) f(7) , we look up the value of f(x) f(x) when x=7 x = 7 .
  2. To find x x such that f(x)=7 f(x) = 7 , we search for the x x value in the table where f(x) f(x) equals 7.
  3. To find f1(9) f^{-1}(9) , we determine the x x value such that f(x)=9 f(x) = 9 .
Step 1: Determine f(7) f(7)

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

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

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

Step 3: Determine f1(9) f^{-1}(9)

To find f1(9) f^{-1}(9) , we need to determine the value of x x such that f(x)=9 f(x) = 9 . From the table, we see that when x=7 x = 7 , f(x)=9 f(x) = 9 .

Final Answer

  • f(7)=9 f(7) = \boxed{9}
  • If f(x)=7 f(x) = 7 , then x=8 x = \boxed{8}
  • f1(9)=7 f^{-1}(9) = \boxed{7}
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