Question

find $f^{-1}(g(-19))$.

$x$	$f(x)$	$g(x)$
$10$	$10$	$9$
$-8$	$17$	$1$
$-19$	$-5$	$-17$
$18$	$-13$	$16$
$-18$	$-4$	$-5$
$-11$	$9$	$11$
$-5$	$-17$	$-19$

Explanation:

Step1: Find \( g(-19) \)

Look at the table for \( g(x) \). When \( x = -19 \), \( g(-19) = -17 \).

Step2: Find \( f^{-1}(-17) \)

We need to find \( x \) such that \( f(x) = -17 \). From the table, when \( f(x) = -17 \), \( x = -5 \) (since \( f(-5) = -17 \)). So \( f^{-1}(-17) = -5 \).

Answer:

\( -5 \)