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

Question

q(x)=-3x+4

r(x)=-4x+3

Find the following.

(r×q)(2)=?

(q×r)(2)=?

Answer 1

With the use of "x", we are assuming multiplication. And, in that case, the other answer to this question by expert tutor Philip P. is perfect!

However, I have a strong suspicion that this question is dealing with function composition. Meaning the "x" should resemble a small circle. If that is true, then the solution will look different.

To first find (r×q)(2) or, as I like to rewrite it, (r(q(2)). This means we'll first have to find q(2):

q(2) = -3(2) + 4 = -6 + 4 = -2

Next we'll use that output as the input for r(x):

r(-2) = -4(-2) + 3 = 8 + 3 = 11

Thus, (r×q)(2) = 11

We'll do a similar process to find (qxr)(2), however the order has now changed. We'll first need to find r(2):

r(2) = -4(2) + 3 = -8 + 3 = -5

Then, we'll use that output as the input for q(x):

q(-5) = -3(-5) + 4 = ?

That answer will be the final result of (qxr)(2).

Again, the solution to your problem depends on what it is asking! If it is function multiplication, then refer to the other answer to this question. If the question refers to function composition, then this is the answer you'll want to reference.

I hope this was helpful!

Answer 2

q(x) = -3x + 4

q(2) = -3(2) + 4 = -6 + 4 = -2

r(x) = -4x + 3

r(2) = -4(2) + 3 = -8 + 3 = -5

(r x q)(2) = r(2) x q(2) = (-2) x (-5) = 10

You try (q x r)(2)