Question

f(x)=.5x+4 ang g(x)=2x-8

find f(g(x)) and g(f(x)). What do you notice?

Answer 1

for f(g(x)) I got x-6 for g(f(x)) I got 4x-12, I don't think that these are right...

Answer 2

its 0.5?

Answer 3

yes

Answer 4

f(g(x))=f(2x-8)=.5(2x-8)+4
=x-4+4
=x

Answer 5

sorry there is 0,5 ???

ok

!!!

Answer 6

g(f(x))= g(0.5x+4)= 2(0.5x+4)-8= x+2-8= x-6

Answer 7

2(0.5x+4)-8= x+8-8

Answer 8

For some reason, I wrote that wrong on my paper, but right on the computer, I put down .05 again...

Answer 9

What are two other functions that are like this?

Answer 10

first, in this case , did u get f(g(x))=g(f(x)) = x ?

Answer 11

I did, and normally I can do this type of problem really easily, but I just didn't get this one

Answer 12

so f(g(x)) = g(f(x))= x implies, f(x) and g(x) are inverses of each other .
another example
f(x) = e^x
g(x) = ln x

Answer 13

In x?

Answer 14

natural logarithm = ln

Answer 15

I don't remember learning about that...

Answer 16

then take other example :
f(x) = \(x^n\)
g(x) = \(\sqrt[n]x\)

Answer 17

ok
thank you so much, it is 3AM, and I am really tired, my brain must not be working or something like that

Answer 18

have a good night's sleep and sweet dreams :)

Answer 19

thanks, I just have a couple more problems and then finally, bed :)

Answer 20

yeah, ask ...

Answer 21

this mapping diagram shows how to find the value of the composite of h and k. Choose one value of x from the first numer line and explain how to find the corresponding value of h(k(x))
the first column represents k(x)=x+1, the second represents k(x), and the third represents h(k)=1/k or h(k(x))

Answer 22

It should be easy, but I don't understand what is being asked...

Answer 23

" how to find the corresponding value of h(k(x))" ... ?
just follow the arrows....
let x=1
k(x)=2, following the arrow
h(k(x)) = 0.5 following the arrow

Answer 24

but what is it asking?

Answer 25

the question : 'Choose one value of x from the first numer line and explain how to find the corresponding value of h(k(x))'
so i chose x=1 , then following the arrows , i got h(k(x))=0.5

Answer 26

So I just had to follow the arrows, I didn't have to use formulas, or multiply the functions or anything?

Answer 27

no, just because the diagram was given, u can follow arrows and get answer, if diagram was not given, then u had to use formulas...

Answer 28

ok

Answer 29

Can you help me with a word problem?

Answer 30

i can try

Answer 31

Lily has a coupon for $10 off, an ad says that there is a 5%discount off on any purchase. Suppose Lily uses the 5% discount on an item, the uses the coupon on the same item. Write the price as a function of x. Write the price as a function of x if she used the coupon first and then the discount. Find c(d(x)) and d(c(x)) Which of these is the function for coupon first? for discount first?

Answer 32

I really just need help writing the functions

Answer 33

I think that c(d(x))=.95x-x-10, using c for coupon first, d for discount first; and that d(c(x)) is (x-10)-9.5x

Answer 34

5% discount on item = x-0.05x = 0.95x
then $10 off --> 0.95 x -10
this is c(d(x)), ok?

Answer 35

ok, so what I had just not -x

Answer 36

yeah, now can u find d(c(x))

Answer 37

It isn't (x-10)-9.5x?

Answer 38

no, $10 off ----> x-10
5% discount = 0.95 (x-10)
d(c(x)) = x-10 - 0.95 (x-10)

Answer 39

discount first---->c(d(x))

Answer 40

So (x-10)-9.5x+95

Answer 41

x-9.5x+85

Answer 42

95?, its 9.5

Answer 43

0.95*10=9.5

Answer 44

ok

Answer 45

how would I remember how to do this if it was a test question?

Answer 46

if u understand, u don't need to remember, just practice.
which part did u not understand ?

Answer 47

I guess that I did understand it, Im just really bad at writing my own functions and stuff like that, I was wondering if there was an easy way to remember how to wrie them

Answer 48

that is it, thanks you soooooooo much hartnn!!! :) you are amazing

Answer 49

goodnight

Answer 50

welcome and good nite :)