Question

find $g(f(8)) - f(f(-8))$ in simplified form:

$x$	$f(x)$	$g(x)$
-8	16	8
-7	10	0
8	5	14
16	18	-4
-11	8	-7
0	19	10
5	12	-11

Explanation:

Step1: Find $f(8)$

From the table, when $x = 8$, $f(8)=5$.

Step2: Find $g(f(8))$

Since $f(8) = 5$, from the table when $x = 5$, $g(5)=- 11$, so $g(f(8))=-11$.

Step3: Find $f(-8)$

From the table, when $x=-8$, $f(-8)=16$.

Step4: Find $f(f(-8))$

Since $f(-8)=16$, from the table when $x = 16$, $f(16)=18$, so $f(f(-8))=18$.

Step5: Calculate $g(f(8))-f(f(-8))$

$g(f(8))-f(f(-8))=-11 - 18=-29$.

Answer:

$-29$