Question

composition of functions

Answer 1

g(f(x))
\[f(x)= \frac{ (x-7) }{ (x+2) } \]
\[g(x)=\frac{ (-2x-7) }{ (x-1) }\]

Answer 2

how would i even begin this?

Answer 3

Oh my, nasty functions. ;-;
Dan, pls.

Answer 4

okay so instead of the place you see x, put f(x) in there

Answer 5

since it is g(f(x))

Answer 6

lol thank you thank clears nothing up .-. i know what to do, but its like bunny said, these are nasty horrible functions

Answer 7

yep it will simplify tho :)

Answer 8

You have to look past that to become good at math. c:
Do what Dan says. Plug in f(x) where you see an x in g(x).

Answer 9

but theres 2 different x's .-.

Answer 10

You plug it into both of them.

Answer 11

g(x) means a function of x, so u see all the operations being on on x in that function
g(f(x)) means a function of f(x)) so you do all those operations on f(x)

Answer 12

\[\frac{ -2\frac{ (x-7) }{ (x+2) } -7 }{ \frac{ (x-7) }{ (x+2) } -1 }\]

Answer 13

go! XD i have no idea what to do

Answer 14

yes

Answer 15

that is right theres nothing else to it

Answer 16

-2(x-7)/(x+2 - 7(x+2)/x+2)
---------------------------
(x-7)/(x+2 - 1((x+2)/x+2)

= -9x
----
-9
= x

Answer 17

so these are inversees right?

Answer 18

?

Answer 19

did common denominator on top and bottom

Answer 20

and simplified

Answer 21

the gx and fx are inverses right

Answer 22

oh yes

Answer 23

do you think you could help me with a few more?

Answer 24

ok sure

Answer 25

f the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi divided by three), what should be used for Xmin and Xmax? Explain your answer.

Answer 26

y=cos (x) has a period of 2pi
y=cos(X/3) has a period 6pi

Answer 27

so 2 period = 12 pi
so, xmin = 0 to Xmax = 12 pi will give us 2 periods

Answer 28

just to confirm
is the problem, y = 5 + 3 cos 2((x - pi)/3)
or y = 5 + 3 cos 2(x - pi/3)

Answer 29

\[5+3\cos 2(x-\frac{ \pi }{ 3 })\]

Answer 30

ok in that case its different

Answer 31

do you mean cos cos^2(x-pi/3)?

Answer 32

what i just wrote was the problem i have

Answer 33

hmm

Answer 34

that is bad form

Answer 35

cos(2(x-pi/3)) = period pi, with a shift to the right of pi/3

Answer 36

so one possible solution is x min =0 and xmax = 2pi

Answer 37

general solution is
the interval (x,x+2pi)

Answer 38

does that make any sense?

Answer 39

what does all that mean? .-.

Answer 40

okay you know what cos x graph looks like right?

Answer 41

yes also what about the 5+3 in front? does that not mean anything

Answer 42

that is a shift in the vertical and an amplitude increase by a factor of 3

Answer 43

this stuff is not for you to memorize though, you can see by* looking at what each transformation would do to your y values or to your base graph y=cos x

Answer 44

oh thank goodness i at least dont have to do that! lol okay thank you c: