Question

the table above gives values of f, f, g, and g for selected values of x. if h(x)=f(g(x)), what is the value of h(1)? a -19 b -14 c 7 d 9

Explanation:

Step1: Apply chain - rule

The chain - rule states that if $h(x)=f(g(x))$, then $h'(x)=f'(g(x))\cdot g'(x)$. We want to find $h'(1)$. First, we need to find $g(1)$. Looking at the table, when $x = 1$, $g(1)=8$.

Step2: Find $f'(g(1))$ and $g'(1)$

Since $g(1)=8$, we find $f'(g(1))=f'(8)$. From the table, $f'(8)=3$. Also, from the table, when $x = 1$, $g'(1)=3$.

Step3: Calculate $h'(1)$

Using the chain - rule $h'(1)=f'(g(1))\cdot g'(1)$. Substitute $f'(8) = 3$ and $g'(1)=3$ into the formula. So $h'(1)=3\times3 = 9$.

Answer:

A. 9