Let's go through each of the questions step-by-step using the provided function values from the table.
1. What is [tex]\( f(8) \)[/tex]?
Look for the value of [tex]\( f \)[/tex] when [tex]\( x = 8 \)[/tex] in the given table:
[tex]\[
f(8) = -7
\][/tex]
Thus, [tex]\( f(8) = -7 \)[/tex].
2. What is [tex]\( f^{-1}(-7) \)[/tex]?
To find [tex]\( f^{-1}(-7) \)[/tex], we need to determine the value of [tex]\( x \)[/tex] such that [tex]\( f(x) = -7 \)[/tex]. From the table, we see:
[tex]\[
f(8) = -7
\][/tex]
Therefore, [tex]\( f^{-1}(-7) = 8 \)[/tex].
3. What is [tex]\( f(6) \)[/tex]?
Look for the value of [tex]\( f \)[/tex] when [tex]\( x = 6 \)[/tex] in the table:
[tex]\[
f(6) = -3
\][/tex]
So, [tex]\( f(6) = -3 \)[/tex].
4. What is [tex]\( f^{-1}(-3) \)[/tex]?
To find [tex]\( f^{-1}(-3) \)[/tex], we need to find the value of [tex]\( x \)[/tex] such that [tex]\( f(x) = -3 \)[/tex]. According to the table:
[tex]\[
f(6) = -3
\][/tex]
Therefore, [tex]\( f^{-1}(-3) = 6 \)[/tex].
In summary, the answers are:
- [tex]\( f(8) = -7 \)[/tex]
- [tex]\( f^{-1}(-7) = 8 \)[/tex]
- [tex]\( f(6) = -3 \)[/tex]
- [tex]\( f^{-1}(-3) = 6 \)[/tex]
