Question

a table of values for f, g, f , and g is given.

x	f(x)	g(x)	f (x)	g(x)
2	1	8	5	7
3	7	2	7	9

(a) if h(x) = f(g(x)), find h(1).
h(1) =
(b) if h(x) = g(f(x)), find h(1).
h(1) =

Explanation:

Step1: Apply chain rule to h(x)

$h'(x) = f'(g(x)) \cdot g'(x)$

Step2: Substitute x=1

$g(1)=2$, $f'(2)=5$, $g'(1)=6$
$h'(1)=5 \cdot 6 = 30$

Step3: Apply chain rule to H(x)

$H'(x) = g'(f(x)) \cdot f'(x)$

Step4: Substitute x=1

$f(1)=3$, $g'(3)=9$, $f'(1)=4$
$H'(1)=9 \cdot 4 = 36$

Answer:

30
36