00:01
This problem gives us functions p of x and q of x, and it wants us to complete a function composition and evaluate the function compositions at 5.
00:08
So first we'll do p of q of 5, which p of q means we want to take the p function and have the input to become q of x.
00:17
So we'll take p of x, which is 2 times x plus 2.
00:21
But instead of the input of x, our input is going to be the entire function of q of x, which is negative 2x squared plus 1.
00:28
Now we can distribute the 2 to simplify, so that's negative 4x squared plus 2 plus 2.
00:34
So just our function composition is negative 4x squared plus 4, and now we can evaluate at 5 by substituting it in for x.
00:44
So that gives us 5 squared, which is 25 times 4, which is negative 100 plus 4.
00:51
So our first evaluation at 5 is negative 96.
00:56
For our next function composition, this time we're doing q of p of 5, which means when we do q of p, that means q's input is now p of x.
01:05
So we'll do the same thing we done the other side, but just reversed.
01:08
Our q of x function is negative 2 times the x value squared plus 1, except our input this time won't be x.
01:15
It'll be the entire 2x plus 2 function...