Suppose that the functions p and q are defined as follows.
p (x) = -x
2
q (x) = -2x +2
Find the following.
(p×q)(-5)
(q ×p)(-5)
If you meant that p(x) = -x/2, then
(p*q)(x) = p(q) = -q/2 = -(-2x+2)/2 = x-1
(q*p)(x) = q(p) = -2p+2 = -2(-x/2)+2 = x+1
Now just use whatever value of x you want
To find the value of (p × q)(-5), we can start by finding the individual values of p(-5) and q(-5), and then multiply them together.
1. Find p(-5):
p(x) = -x^2
p(-5) = -(-5)^2
p(-5) = -25
2. Find q(-5):
q(x) = -2x + 2
q(-5) = -2(-5) + 2
q(-5) = 10 + 2
q(-5) = 12
3. Multiply p(-5) and q(-5):
(p × q)(-5) = p(-5) * q(-5)
(p × q)(-5) = (-25) * (12)
(p × q)(-5) = -300
Therefore, (p × q)(-5) is equal to -300.
Now let's find (q × p)(-5) using the same steps:
1. Find q(-5):
q(x) = -2x + 2
q(-5) = -2(-5) + 2
q(-5) = 10 + 2
q(-5) = 12
2. Find p(-5):
p(x) = -x^2
p(-5) = -(-5)^2
p(-5) = -25
3. Multiply q(-5) and p(-5):
(q × p)(-5) = q(-5) * p(-5)
(q × p)(-5) = (12) * (-25)
(q × p)(-5) = -300
Therefore, (q × p)(-5) is also equal to -300.
To find (p × q)(-5), we need to evaluate the product of the two functions p and q at x = -5.
1. First, let's substitute x = -5 into the function p(x) = -x²:
p(-5) = -(-5)²
= -(25)
= -25
2. Then, substitute x = -5 into the function q(x) = -2x + 2:
q(-5) = -2(-5) + 2
= 10 + 2
= 12
3. Finally, we find the product of p(-5) and q(-5):
(p × q)(-5) = p(-5) × q(-5)
= -25 × 12
= -300
Next, to find (q × p)(-5), we need to evaluate the product of the two functions q and p at x = -5.
1. First, substitute x = -5 into the function q(x) = -2x + 2:
q(-5) = -2(-5) + 2
= 10 + 2
= 12
2. Then, substitute x = -5 into the function p(x) = -x²:
p(-5) = -(-5)²
= -(25)
= -25
3. Finally, we find the product of q(-5) and p(-5):
(q × p)(-5) = q(-5) × p(-5)
= 12 × (-25)
= -300
Therefore, (p × q)(-5) = (q × p)(-5) = -300.