Question

p(x) = -4x - 3
q(x) = 3x + 2
find the following.
(p ∘ q)(-4) =
(q ∘ p)(-4) =

Explanation:

for \((p \circ q)(-4)\):

Step1: Find \(q(-4)\)

First, we need to find the value of \(q(x)\) when \(x = -4\). The function \(q(x)=3x + 2\), so substitute \(x=-4\) into \(q(x)\):
\(q(-4)=3\times(-4)+2=-12 + 2=-10\)

Step2: Find \(p(q(-4))\)

Now, we substitute the result of \(q(-4)\) into the function \(p(x)\). The function \(p(x)=-4x-3\), and we know \(q(-4)=-10\), so substitute \(x = -10\) into \(p(x)\):
\(p(-10)=-4\times(-10)-3 = 40-3=37\)
So, \((p\circ q)(-4)=37\)

for \((q \circ p)(-4)\):

Step1: Find \(p(-4)\)

First, find the value of \(p(x)\) when \(x=-4\). The function \(p(x)=-4x - 3\), substitute \(x = -4\) into \(p(x)\):
\(p(-4)=-4\times(-4)-3=16 - 3 = 13\)

Step2: Find \(q(p(-4))\)

Now, substitute the result of \(p(-4)\) into the function \(q(x)\). The function \(q(x)=3x + 2\), and we know \(p(-4)=13\), so substitute \(x = 13\) into \(q(x)\):
\(q(13)=3\times13+2=39 + 2=41\)
So, \((q\circ p)(-4)=41\)

Answer:

\((p \circ q)(-4)=\boxed{37}\)
\((q \circ p)(-4)=\boxed{41}\)