use the chart to find ( h(4) ) in simplest form.\n\n h(x)=f(g(x)) \n\nanswer\n\n( h(4)= )

Explanation:

Step1: Apply the chain rule

The chain rule states that if (h(x) = f(g(x))), then (h'(x)=f'(g(x))\cdot g'(x)).

Step2: Substitute (x = 4)

When (x = 4), we first find (g(4)) from the table. (g(4)=3). Then (h'(4)=f'(g(4))\cdot g'(4)).

Step3: Use the table values

Since (g(4) = 3), (f'(g(4))=f'(3)) and (g'(4) = 7). From the table, (f'(3)=1). So (h'(4)=f'(3)\cdot7).

Step4: Calculate the result

Substitute (f'(3) = 1) into the expression. (h'(4)=1\times7).

Answer:

(7)