Question

suppose that the functions p and q are defined as follows. p(x)=2x+3 q(x)=5x-3 find the following. (p ∘q)(-3) = (q ∘p)(-3) =

Explanation:

Step1: Compute $q(-3)$

$q(-3)=5(-3)-3=-15-3=-18$

Step2: Compute $p(q(-3))$

$p(-18)=2(-18)+3=-36+3=-33$

Step3: Compute $p(-3)$

$p(-3)=2(-3)+3=-6+3=-3$

Step4: Compute $q(p(-3))$

$q(-3)=5(-3)-3=-15-3=-18$

Answer:

$(p \circ q)(-3) = -33$
$(q \circ p)(-3) = -18$