Question

1. let $g(x) = 2x$ and $h(x) = x^2 + 4$. evaluate $(h \circ g)(-2)$. \bigcirc 16 \bigcirc -16 \bigcirc 20 \bigcirc -12

Explanation:

Step1: Understand function composition

The composition \((h \circ g)(x)\) means \(h(g(x))\). So first, we need to find \(g(-2)\), then substitute that result into \(h(x)\).

Step2: Calculate \(g(-2)\)

Given \(g(x) = 2x\), substitute \(x = -2\) into \(g(x)\):
\(g(-2)=2\times(-2)= -4\)

Step3: Calculate \(h(g(-2)) = h(-4)\)

Given \(h(x)=x^{2}+4\), substitute \(x = -4\) into \(h(x)\):
\(h(-4)=(-4)^{2}+4\)
First, calculate \((-4)^{2}\), which is \(16\) (because a negative number squared is positive). Then add \(4\):
\(16 + 4 = 20\)

Answer:

20