Functions help! I've never seen this type of problem before!?

Question

I have no idea what to call this so I can't look it up... I need to know what this is called and how to solve it if possible:

Consider the function f(x)=x^2-9x

a)Find (F○F)(5)
b)Find (F○F○F)(-1)

Solutions:
a)580
b)10

Answer 1

(f o f)(5) = f(f(5)) ... this is called composition of functions
now..f(5) = 25 - 45 = -20
thus (f o f)(5) = f(-20) = 400 + 180 = 580


do the same for the next question...
its f(f(f(-1)))


§

Answer 2

F o F is a short way of saying function f of f.

It means take the output of the function and feed it back into the function again.

(F○F)(5) = f(f(5))

First figure f(5) = (5)² - 9(5) = 25 - 45 = -20
Now figure f(-20) = (-20)² - 9(-20) = 400 + 180 = 580

Same for the next problem, but with 3 steps:
(F○F○F)(-1) = f(f(f(-1)))

f(-1) = (-1)² -9(-1) = 1 + 9 = 10
f(10) = (10)² - 9(10) = 100 - 90 = 10
f(10) = 10

P.S. Can you tell me what (F○F○F○F○F○F○F○F○F)(-1) would be? :-D

Answer 3

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Answer 4

a)
it wants to know the "function of". So what you just do is plug 5 into the f(x) equation and get -20. Now take -20 and plug it again into the f(x) equation and you'll end up with 580.

b)
this one is worked the same way, but it wants you to plug it in three times. just plug -1 into f(x) and get:

f(-1) = 10
then take 10 and plug it into the f(x) again.

f(10) = 10

and finally plug it in again and get:

f(10) = 10

Answer 5

g∘f indicates a composition function. It means "apply function f, then apply function g to the result."