Question

Given p(x) = -2x + 1 and q(x) = -x^2, find the following.

(p•q)(1) =

a) -3
b) 3
c) 0
d) -1

(q•p)(1) =

a) -3
b) 3
c) 0
d) -1

Answer 1

The product (p•q)(1) and (q•p)(1), where p(x) = -2x + 1 and q(x) = -x^2, both evaluate to 1 when x is substituted with 1. The multiplication of these functions is commutative, hence they yield the same result.

Step-by-step explanation:

The student is asking to calculate the product of two functions evaluated at a certain point, specifically (p•q)(1) and (q•p)(1), where p(x) = -2x + 1 and q(x) = -x^2. Let's first find the product of these functions.

Product of p(x) and q(x) is (p•q)(x) = p(x) • q(x).
Thus, (p•q)(x) = (-2x + 1) • (-x^2).
To evaluate this at x=1, substitute 1 for x:
(p•q)(1) = (-2• 1 + 1) • (-(1)^2).
(p•q)(1) = (-2 + 1) • (-1).
(p•q)(1) = (-1) • (-1).
(p•q)(1) = 1.

As for (q•p)(1), it will yield the same result since the multiplication of functions is commutative. Thus, (q•p)(1) = 1 as well.

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