Question

find $f(4) + 4f^{-1}(-7)$.\
\

$x$	$f(x)$	\
---	---	\
9	$-7$	\
$-3$	4	\
1	7	\
4	9

Explanation:

Step1: Find \( f(4) \)

From the table, when \( x = 4 \), \( f(4)=9 \).

Step2: Find \( f^{-1}(-7) \)

The inverse function \( f^{-1}(y) \) gives the \( x \) such that \( f(x)=y \). From the table, when \( f(x)= - 7 \), \( x = 9 \), so \( f^{-1}(-7)=9 \).

Step3: Calculate \( f(4)+4f^{-1}(-7) \)

Substitute \( f(4) = 9 \) and \( f^{-1}(-7)=9 \) into the expression:
\( f(4)+4f^{-1}(-7)=9 + 4\times9 \)
\(=9+36\)
\(=45\)

Answer:

\( 45 \)