Question

The table below shows some inputs and outputs of the invertible function
\[f\] with domain all real numbers.
\[x\]
\[ 14 \]
\[ -6 \]
\[ -1 \]
\[ 10 \]
\[ -10 \]
\[ 3 \]
\[f(x)\]
\[ 7 \]
\[ -10 \]
\[ -15 \]
\[ 14 \]
\[ -4 \]
\[ -9 \]
Find the following values:
\[f^{-1}(f^{-1}(7))=\]
\[ f^{-1}(-4)=\]

Answer 1

From the table f(14)=7, so f^{-1}(7)=14. Then f^{-1}(14)=10 (since f(10)=14). Thus
f^{-1}(f^{-1}(7)) = 10.

Also, f(-10) = -4, so f^{-1}(-4) = -10.