Let's analyze the table and address the questions step-by-step.
### Step 1: Evaluate [tex]\( f(1) \)[/tex]
To evaluate [tex]\( f(1) \)[/tex], we need to find the value in the table where [tex]\( x = 1 \)[/tex]. Looking at the table:
[tex]\[
\begin{array}{|c|r|r|r|r|r|r|r|r|r|r|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
f(x) & 96 & 75 & 46 & 59 & 13 & 79 & 4 & 28 & 1 & 11 \\
\hline
\end{array}
\][/tex]
For [tex]\( x = 1 \)[/tex], the corresponding [tex]\( f(x) \)[/tex] value is [tex]\( 75 \)[/tex]. Therefore:
[tex]\[
f(1) = 75
\][/tex]
### Step 2: Solve [tex]\( f(x) = 4 \)[/tex]
To solve [tex]\( f(x) = 4 \)[/tex], we need to look for the value of [tex]\( x \)[/tex] where [tex]\( f(x) = 4 \)[/tex] in the table. Scanning through the [tex]\( f(x) \)[/tex] values:
[tex]\[
\begin{array}{|c|r|r|r|r|r|r|r|r|r|r|}
\hline
x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
f(x) & 96 & 75 & 46 & 59 & 13 & 79 & 4 & 28 & 1 & 11 \\
\hline
\end{array}
\][/tex]
We see that [tex]\( f(x) = 4 \)[/tex] when [tex]\( x = 6 \)[/tex]. Therefore:
[tex]\[
x = 6
\][/tex]
### Summary
- The value of [tex]\( f(1) \)[/tex] is [tex]\( 75 \)[/tex].
- The solution to [tex]\( f(x) = 4 \)[/tex] is [tex]\( x = 6 \)[/tex].
So, the final results are:
[tex]\[
f(1) = 75 \quad \text{and} \quad x = 6 \text{ when } f(x) = 4.
\][/tex]
