Question

question 8 - 1 point suppose ( h(x)=f(g(x)) ). given the table of values below, determine ( h(-1) ). do not include \ ( h(-1)=) \ in your answer. provide your answer below:

( x )	( -1 )	( 3 )	( 5 )
( g(x) )	( 3 )	( 4 )	( -4 )
( f(x) )	( -6 )	( 5 )	( -4 )
( g(x) )	( -7 )	( 2 )	( -5 )

Explanation:

Step1: Apply chain - rule

$h'(x)=f'(g(x))\cdot g'(x)$

Step2: Find $g(-1)$

From table, $g(-1) = 3$

Step3: Calculate $h'(-1)$

$h'(-1)=f'(g(-1))\cdot g'(-1)=f'(3)\cdot g'(-1)$. From table, $f'(3)=5$ and $g'(-1)= - 7$, so $h'(-1)=5\times(-7)=-35$

Answer:

$-35$