Question

use the table below to fill in the missing values.
\begin{array}{|c|c|}hline x&f(x)\hline0&4\hline1&3\hline2&7\hline3&2\hline4&1\hline5&8\hline6&9\hline7&5\hline8&6\hline9&0\hlineend{array}
f(2)=\\
if f(x)=6, then x =\\
f^{-1}(7)=\\
if f^{-1}(x)=8, then x =\\
question help: video

Explanation:

Step1: Find f(2)

Look for x = 2 in the table. When x = 2, f(x)=7.

Step2: Find x when f(x) = 6

Search the f(x) - column for 6. When f(x)=6, x = 8.

Step3: Find \(f^{-1}(7)\)

The inverse function \(f^{-1}(y)\) gives the x - value for which f(x)=y. When y = 7, from the table x = 2, so \(f^{-1}(7)=2\).

Step4: Find x when \(f^{-1}(x)=8\)

If \(f^{-1}(x)=8\), then from the table when x = 6, \(f(8)=6\), so \(f^{-1}(6)=8\) and x = 6.

Answer:

f(2) = 7
if f(x) = 6, then x = 8
\(f^{-1}(7)=2\)
if \(f^{-1}(x)=8\), then x = 6