Question

use the chart to find h(4) in simplest form.

x	f(x)	f(x)	g(x)	g(x)
12	12	-1	6	-9

h(x)=f(g(x))
answer attempt 1 out of 1
h(4)=

Explanation:

Step1: Apply chain - rule

The chain - rule states that if $h(x)=f(g(x))$, then $h^{\prime}(x)=f^{\prime}(g(x))\cdot g^{\prime}(x)$.

Step2: Evaluate at $x = 4$

We need to find $h^{\prime}(4)$, so we substitute $x = 4$ into the chain - rule formula: $h^{\prime}(4)=f^{\prime}(g(4))\cdot g^{\prime}(4)$.

Step3: Find $g(4)$ and $g^{\prime}(4)$ from the table

From the table, when $x = 4$, $g(4)=12$ and $g^{\prime}(4)=-2$.

Step4: Find $f^{\prime}(g(4))$

Since $g(4)=12$, we need to find $f^{\prime}(12)$. From the table, when $x = 12$, $f^{\prime}(12)=-1$.

Step5: Calculate $h^{\prime}(4)$

Substitute $f^{\prime}(g(4))=-1$ and $g^{\prime}(4)=-2$ into the formula $h^{\prime}(4)=f^{\prime}(g(4))\cdot g^{\prime}(4)$. So $h^{\prime}(4)=(-1)\times(-2)=2$.

Answer:

$2$