Question

question
find $f^{-1}(f(-8)) - 3f(f(-7))$.

Explanation:

Step1: Evaluate \( f^{-1}(f(-8)) \)

By the property of inverse functions, \( f^{-1}(f(x)) = x \) for all \( x \) in the domain of \( f \). So, when \( x = -8 \), we have \( f^{-1}(f(-8))=-8 \).

Step2: Evaluate \( f(-7) \)

From the table, when \( x = -7 \), \( f(-7)=-4 \).

Step3: Evaluate \( f(f(-7)) \)

Since \( f(-7) = -4 \), we need to find \( f(-4) \). From the table, when \( x = -4 \), \( f(-4)=7 \). So, \( f(f(-7)) = f(-4)=7 \).

Step4: Evaluate \( 3f(f(-7)) \)

We know \( f(f(-7)) = 7 \), so \( 3f(f(-7))=3\times7 = 21 \).

Step5: Evaluate the entire expression

Now, substitute the values we found into \( f^{-1}(f(-8)) - 3f(f(-7)) \):
\( -8-21=-29 \)

Answer:

\(-29\)