SOLUTION: I've been wrapping my head around this for a while and would like an easier explanation to solving these functions. Thank-you. Suppose that the functions p and q are defined as

Algebra ->  Functions -> SOLUTION: I've been wrapping my head around this for a while and would like an easier explanation to solving these functions. Thank-you. Suppose that the functions p and q are defined as       Log On


   

Question 1123452: I've been wrapping my head around this for a while and would like an easier explanation to solving these functions. Thank-you.
Suppose that the functions p and q are defined as follows.
p(x)= x^2+9
q(x)= √x+8
Find:
(p ∘ q)(8) =
(q ∘ p)(8) =
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
p o q put q into wherever there is a x. So the x^2 becomes (q's function^2) then add 9.
sqrt(x+8)^2+9=x+8+9=x+17 and when x=8, the function equals 25
q o p put p into q wherever there is a x. So the sqrt (x+8) becomes sqrt (x^2+9 then +8)
sqrt(x^2+9+8)=sqrt(x^2+17), so when x=8 sqrt (81)=9

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let's say you have a function

Then





as long as



as long as

The function is EXACTLY the same thing as saying . In other words, take the definition of and every place you see an put the definition of in its place.



Then for just plug in 8 and do the arithmetic. Hint: For the exact answer is simplest form use

Do the other one the same way.

By the way, this solution is incorrect if you actually meant instead of . If this is the case, it is on you because you failed to put parentheses around the radicand in the definition of . My interpretation is correct based on what you wrote.


John

My calculator said it, I believe it, that settles it