Suppose that the functions p and q are defined as follows.
p(x)=x+1
q(x)=-x^2-1
Find the following.
(pxq)(-3)
(qxp)(-3)
do you mean
p ( q(-3) ) ?
if so
q(-3) = -9-1 = -10
p(-10) = -10+1 = -9
and
p(-3) = -3+1 = -2
q(-2) = -2-1 = -5
To find (pxq)(-3), we need to begin by evaluating the function p(x) and function q(x) separately.
- For p(x), the function is defined as p(x) = x + 1. To evaluate p(x) at x = -3, substitute -3 into the function:
p(-3) = (-3) + 1 = -2
- For q(x), the function is defined as q(x) = -x^2 - 1. To evaluate q(x) at x = -3, substitute -3 into the function:
q(-3) = -(-3)^2 - 1 = -9 - 1 = -10
Now that we have the values of p(-3) = -2 and q(-3) = -10, we can proceed to find (pxq)(-3) by multiplying the two values together:
(pxq)(-3) = (-2) * (-10) = 20
Now let's find (qxp)(-3) by switching the order of the functions:
- For q(x), the function is still q(x) = -x^2 - 1. To evaluate q(x) at x = -3, substitute -3 into the function:
q(-3) = -(-3)^2 - 1 = -9 - 1 = -10
- For p(x), the function is still p(x) = x + 1. To evaluate p(x) at x = -3, substitute -3 into the function:
p(-3) = (-3) + 1 = -2
Now that we have the values of q(-3) = -10 and p(-3) = -2, we can proceed to find (qxp)(-3) by multiplying the two values together:
(qxp)(-3) = (-10) * (-2) = 20
Therefore, (pxq)(-3) = 20 and (qxp)(-3) = 20.