Question

Suppose that the functions p and q are defined as follows:
p(x)=-2x+1
q(x)=-x^2

Find the following

p o q(-5)=10x^3
q o p(-5)=2x^3-5

Iis this right?

Answer 1

Hmm... you've reversed the two answers, I suppose!

Answer 2

But that isn't correct either. Well, let's approach this step-by-step!

Answer 3

You need to find p of q of -5. Or,\[p(\color{blue}{q(-5)})\]So, we first find what q(-5) is -- then we do the \(p\) of that.

Answer 4

so, 5x^2-2x?

Answer 5

Yeah, but you are not to find p o q (x), but p o q (-5).

Answer 6

so p o q(-5) isn't -2x-1*(-x^2(-5)
and
q o p isn't -x^2(-2x-1(-5))?

Answer 7

Hmm, not really.

p o q(-5) means \(p(\color{blue}{q(-5)})\). So what this means is:

First, find q(-5).
Then, find the p of what you get.

Answer 8

q(-5) is when you plug in -5 instead of \(x\).

Answer 9

Are you following it?

Answer 10

I don't think so. what would it look like?

Answer 11

\[q(\color{blue}x) =-\color{blue}x^2\]\[q(-5) = -(-5)^2\]

Answer 12

Does that make sense?

Answer 13

so the answers would be poq(-5) 25-2x and 2x^2+1 qop(-5)

Answer 14

Again, remember that it is not poq(x), but poq(-5).