Suppose that the functions p and q are defined as follows.
p(x)=-x-1
q(x)=-2x^2-2
Find the following.
(pxq)(5)
(qxp)(5)
stop using x as both a variable and an operator. I see this question was already interpreted and answered, but now you post it again. So maybe you meant (p*q)(5). If so, then
p(x)*q(x) = (-x-1)(-2x^2-2) = 2(x^3 + x^2 + x + 1) = 2(x^4 - 1)/(x-1)
(p*q)(5) = 2(624)/4 = 312
Or, p(5) = -6, q(5) = -52 so (p*q)(5) = (-6)*(-52) = 312
and, since multiplication is commutative, this is also (q*p)(5)
so, maybe you did mean it the way that it was explained to "Froggy" a couple of questions below.
To find (pxq)(5), we need to evaluate the product of p(x) and q(x) at x = 5.
Step 1: Substitute x = 5 into p(x) and q(x).
p(5) = -(5) - 1 = -6
q(5) = -2(5^2) - 2 = - 52
Step 2: Multiply the values obtained in Step 1.
(pxq)(5) = p(5) * q(5) = -6 * -52 = 312
Therefore, (pxq)(5) = 312.
To find (qxp)(5), we need to evaluate the product of q(x) and p(x) at x = 5.
Step 1: Substitute x = 5 into q(x) and p(x).
q(5) = -2(5^2) - 2 = - 52
p(5) = -(5) - 1 = -6
Step 2: Multiply the values obtained in Step 1.
(qxp)(5) = q(5) * p(5) = -52 * -6 = 312
Therefore, (qxp)(5) = 312.
To find (pxq)(5), we need to evaluate the function p(x) at x=5 and multiply the result by q(x) evaluated at the same value. Here are the steps:
Step 1: Evaluate p(x) at x=5:
p(5) = -5 - 1 = -6
Step 2: Evaluate q(x) at x=5:
q(5) = -2(5)^2 - 2 = -2(25) - 2 = -50 - 2 = -52
Step 3: Multiply p(5) by q(5):
(pxq)(5) = p(5) * q(5) = (-6) * (-52) = 312
Therefore, (pxq)(5) = 312.
To find (qxp)(5), we need to evaluate the function q(x) at x=5 and multiply the result by p(x) evaluated at the same value. Here are the steps:
Step 1: Evaluate q(x) at x=5:
q(5) = -2(5)^2 - 2 = -2(25) - 2 = -50 - 2 = -52
Step 2: Evaluate p(x) at x=5:
p(5) = -5 - 1 = -6
Step 3: Multiply q(5) by p(5):
(qxp)(5) = q(5) * p(5) = (-52) * (-6) = 312
Therefore, (qxp)(5) = 312.