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

question suppose $h(x)=f(g(x))$. given the table of values below, determine $h(2)$. \n|$x$|$f(x)$|$g(x)$|$f(x)$|$g(x)$|\n|----|----|----|----|----|\n|$2$|$-2$|$3$|$5$|$5$|\n|$3$|$-1$|$6$|$5$|$-4$|\n|$5$|$-4$|$-5$|$2$|$-2$|\ndo not include \$h(2)=$\ in your answer. provide your answer below:

question suppose $h(x)=f(g(x))$. given the table of values below, determine $h(2)$. \n|$x$|$f(x)$|$g(x)$|$f(x)$|$g(x)$|\n|----|----|----|----|----|\n|$2$|$-2$|$3$|$5$|$5$|\n|$3$|$-1$|$6$|$5$|$-4$|\n|$5$|$-4$|$-5$|$2$|$-2$|\ndo not include \$h(2)=$\ in your answer. provide your answer below:

Answer

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