Answer:
Step-by-step explanation:
To find (q ∘ p)(2) and (p ∘ q)(2), we first need to understand the operation "∘" which means composition of functions. In this case, we need to apply one function after another. Let's break it down step by step.
1. First, let's write down the expressions for functions P(x) and Q(x):
P(x) = -3x + 4
Q(x) = 2x - 2
2. Now, let's find (q ∘ p)(2) which means we need to first apply function P(x) to 2 and then apply function Q(x) to the result.
Step 2.1: Apply P(x) to 2:
P(2) = -3(2) + 4 = -6 + 4 = -2
Step 2.2: Apply Q(x) to the result from Step 2.1:
Q(-2) = 2(-2) - 2 = -4 - 2 = -6
So, (q ∘ p)(2) = -6.
3. Next, let's find (p ∘ q)(2) which means we need to first apply function Q(x) to 2 and then apply function P(x) to the result.
Step 3.1: Apply Q(x) to 2:
Q(2) = 2(2) - 2 = 4 - 2 = 2
Step 3.2: Apply P(x) to the result from Step 3.1:
P(2) = -3(2) + 4 = -6 + 4 = -2
So, (p ∘ q)(2) = -2.
In summary:
(q ∘ p)(2) = -6
(p ∘ q)(2) = -2
