Question

use the graph of f(x), selected values of a linear function g(x) in the table, and the equation h(x) to evaluate (h ⋅ g)(-1). x g(x) -3 -5 -1 -1 0 1 4 9 h(x) = x² - 4 -5 -3 3 5

Explanation:

Step1: Recall the definition of function multiplication

The product of two functions \((h\cdot g)(x)\) is defined as \(h(x)\cdot g(x)\). So, to find \((h\cdot g)(-1)\), we need to find \(h(-1)\) and \(g(-1)\) first, then multiply them.

Step2: Find \(g(-1)\) from the table

Looking at the table for \(g(x)\), when \(x = -1\), \(g(-1)=-1\).

Step3: Find \(h(-1)\) using the equation \(h(x)=x^{2}-4\)

Substitute \(x = -1\) into \(h(x)\):
\(h(-1)=(-1)^{2}-4\)
\(= 1 - 4\)
\(=-3\)

Step4: Multiply \(h(-1)\) and \(g(-1)\)

\((h\cdot g)(-1)=h(-1)\cdot g(-1)=(-3)\cdot(-1)\)
\(= 3\)

Answer:

3