Question

@freckles the fraction is throwing me off with this one. but i may be able to do it!

Answer 1

so im going to replace the g(x) in this one?

Answer 2

f(g(x)) is the first question

Answer 3

f(g(x)) means replace the x's in f with g(x)

Answer 4

so f(2-x)

Answer 5

yes which equals ?

Answer 6

umm... im blanking :/

Answer 7

9/x^5(2-x)?

Answer 8

well f(2-x) means replace the x's in f with (2-x)

Answer 9

OH!

Answer 10

f(x)=9/x^5
you see the x's there?
replace them with (2-x)

Answer 11

f(x)=9/(2-x)^5

Answer 12

right

Answer 13

so that means 9/64-x^5

Answer 14

oh no no

Answer 15

expanding (2-x)^5 is much uglier than that
and true me it is no good to do here

Answer 16

trust me*

Answer 17

\[(2-x)^5=2^5+5(-x)(2)^4+10(-x)^2(2)^3+10(-x)^3(2)^2+5(-x)^4(2)+(-x)^5\]
which doesn't equal 64-x^5

Answer 18

oh gosh

Answer 19

so what I'm saying is just leave it as (2-x)^5

Answer 20

oh we can do that?

Answer 21

totally

Answer 22

ok! so i guess its on to the next one! i did a few on my own but theres a kind of word problem now...

Answer 23

oh! domain!

Answer 24

umm equal to zero?

Answer 25

so 9/(2-x)^5=0

Answer 26

i dont know where to go from that

Answer 27

do you remember in fractions you cannot have the denominator is 0?
there is the denominator 0 here?

Answer 28

2!

Answer 29

when is the denominator 0 here?

Answer 30

yes

Answer 31

has to be above 2!

Answer 32

[3,inf)

Answer 33

well you have any real number except 2

Answer 34

(-inf,2) union (2,inf)

Answer 35

oh! the unions ok i never did use those...

Answer 36

oh wait theres a second part to this LOL

Answer 37

g(f(x))

Answer 38

so we're making it g(9/x^5)

Answer 39

ok

Answer 40

so you are replacing the x's in g with f(x)

Answer 41

yes

Answer 42

and yes you are left with finding g(9/x^5)

Answer 43

so where do we go from there?

Answer 44

if you have w(h(x))
you are just going to replace all the x's in w with h(x)

so here you are going to replace all the x's you have in g(x) with 9/x^5

recall g(x)=2-x

Answer 45

2-9/x^5

Answer 46

yea

Answer 47

-7/x^5

Answer 48

no you do not have a common denominator

Answer 49

I mean if you want to combine them you would have to find a common denominator

Answer 50

but it is not necessary to try to combine the fractions

Answer 51

so we can keep them separate?

Answer 52

yep

Answer 53

so it would be .... what? cause we got rid of the -2 didnt we? where would its denom go?

Answer 54

2**

Answer 55

what

Answer 56

dont we only have one frac?

Answer 57

wait im confused now

Answer 58

you found your function earlier

Answer 59

2-9/x^5

Answer 60

correct

Answer 61

\[g(f(x))=2-\frac{9}{x^5}\]

Answer 62

oh! i just keep it! OK!

Answer 63

i was trying to solve it lol

Answer 64

solve what?

Answer 65

you mean you were trying to combine the fractions?

Answer 66

it is not necessary but you could if you multiply 2 by x^5/x^5

Answer 67

ya i was trying to combine. The domain wouldnt be (-inf,1]U[1,inf) would it?

Answer 68

no you only have that one fraction
and remember you cannot divide by 0

Answer 69

x^5 is zero when x=?

Answer 70

0?

Answer 71

right

Answer 72

so include everything but x=0

Answer 73

oh i wrote it wrong!

Answer 74

i need to replace the 1 with a zero!

Answer 75

(-inf,0) union (0,inf)

just like before we are going to put a ) after the 0 in the first interval and a ( before the other 0
this means we are not including x=0

if we had brackets however that means we are including but as I said we do not want to include x=0

Answer 76

you must get rid of those brackets

Answer 77

also

Answer 78

anyways I must go
good luck on the rest of your problems

Answer 79

thanks for the help ^_^ i finished it just enough to get a feel for the test! and i bookmarked all the questions to go back and study! :3 if i have anymore questions ill certainly be coming back!

Answer 80

cool stuff :)

Answer 81

have fun

Answer 82

have a nice night!