Question

Suppose that the functions p and q are defined as follows.

p(x) = x² + 7
q(x) = √(x + 8)
Find the following:
A. (P • q ) (1)
B. (Q • p) (1)

Answer 1

To find (P • q) (1) and (Q • p) (1), we calculate p(1) and q(1) separately, then multiply these values. Both compositions result in the same value of 24.

Step-by-step explanation:

To solve for A. (P • q ) (1) and B. (Q • p) (1), we first evaluate each function separately at x=1. For p(x) = x² + 7, substitute 1 for x to get p(1) = 1² + 7 = 8. For q(x) = √(x + 8), substitute 1 for x to get q(1) = √(1 + 8) = √9 = 3.

Now we can calculate each requested composition. For A. (P • q) (1), multiply p(1) by q(1) to get (8) • (3) = 24. Similarly, for B. (Q • p) (1), multiply q(1) by p(1) which is the same as A, so (3) • (8) = 24.

Both (P • q) (1) and (Q • p) (1) are equal, resulting in the same answer of 24.