Question

question suppose $h(x)=f(g(x))$. given the table of values below, determine $h(2)$.

$x$	$f(x)$	$g(x)$	$f(x)$	$g(x)$
$3$	$-1$	$6$	$5$	$-4$
$5$	$-4$	$-5$	$2$	$-2$

do not include \$h(2)=$\ in your answer. provide your answer below:

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 $x = 2$

When $x = 2$, we first find $g(2)=3$ from the table. Then we find $f^{\prime}(g(2))=f^{\prime}(3)$ and $g^{\prime}(2)$. From the table, $f^{\prime}(3) = 5$ and $g^{\prime}(2)=5$.

Step3: Calculate $h^{\prime}(2)$

$h^{\prime}(2)=f^{\prime}(g(2))\cdot g^{\prime}(2)=5\times5 = 25$.

Answer:

25