CabelaK43841 CabelaK43841
  • 03-11-2022
  • Mathematics
contestada

Suppose that the functions p and q are defined as follows.p(x) = -2x-1q(x)=x²+1Find the following.(q*p)(-2)=(p*q)(-2)=

Respuesta :

EliiJ497241 EliiJ497241
  • 03-11-2022

Answer:

(a)10

(b)-11

Explanation:

Given the function p(x) and q(x) defined as follows:

[tex]\begin{gathered} p(x)=-2x-1 \\ q(x)=x^2+1 \end{gathered}[/tex]

Part A

[tex]\begin{gathered} (q\circ p)(x)=q(p(x)) \\ =(-2x-1)^2+1 \\ (q\circ p)(-2)=(-2(-2)-1)^2+1 \\ =(4-1)^2+1 \\ =3^2+1 \\ (q\circ p)(-2)=10 \end{gathered}[/tex]

Part B

[tex]\begin{gathered} (p\circ q)(x)=p(q(x)) \\ =-2(x^2+1)-1 \\ (p\circ q)(-2)=-2((-2)^2+1)-1 \\ =-2(4+1)-1 \\ =-2(5)-1=-10-1 \\ (p\circ q)(-2)=-11 \end{gathered}[/tex]

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