Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x)=4/x and g(x)=4/x

Answer 1

@jim_thompson5910 this is the last question on my homework for the weekend... Please help me!!!

Answer 2

How far did you get?

Answer 3

I have no clue how to start this one... It says they're supposed to be inverses but they''re the same...

Answer 4

what is f(g(x))?

Answer 5

x

Answer 6

well that's what you have to show

Answer 7

but how would you show it?

Answer 8

by multiplying f(x) and g(x)?

Answer 9

no

Answer 10

that's if they wanted f(x) * g(x)

Answer 11

okay then I'm not entirely sure...

Answer 12

an example of f(g(x))

let f(x) = 2x+3 and g(x) = x^4

---------------------------------

f(x) = 2x + 3 ... start with the outer function

f(g(x)) = 2*g(x) + 3 ... replace ALL copies of x with g(x)

f(g(x)) = 2x^4 + 3 ... replace ALL copies of g(x) on the right side with x^4 (since g(x) = x^4)

Answer 13

So that means if f(x) = 2x+3 and g(x) = x^4, then f(g(x)) = 2x^4 + 3

Answer 14

okay, I got \[f(g(x))=\frac{ 4 }{ \frac{ 4 }{ x } }\] but I think that's wrong...

Answer 15

Lol I have a doubt, I got 4/4/x which I'm not sure is right.

But knowing that they're asking they they both equal the same g(f(x)) would also = 4/4/x which make me unsure of my answer. I'm 50/50 :p

Answer 16

yeah, that's the same thing I got.... @jim_thompson5910 is that right?

Answer 17

think of that first uppermost 4 as 4/1

Answer 18

you will then have 4/1 over 4/x

so divide those fractions and tell me what you get

Answer 19

okay...?

Answer 20

that's the same as 4/1 * x/4 right?

Answer 21

Well i think its actually right, as it would be 4 would be 4/1 divided by 4/x or 4/1

Or 4/1 * 1/4 = 4/4 = 1

Idk lol I was learning the inverse at the same time which is what set me off :P

Answer 22

OH! The 4s cancel out and you're left with 1x or just x!!!! right?

Answer 23

keep going Sunshine447

Answer 24

good, you got it

Answer 25

Yes :)

Answer 26

@jim_thompson5910 , how do you say f(^-1) ? I keep forgetting it.

Answer 27

now how does this make them inverse?

Answer 28

you've just shown that f(g(x)) = x

now you need to show that g(f(x)) = x

Answer 29

if you can show that f(g(x)) = x and g(f(x)) = x are both true, then f(x) and g(x) are inverses of one another

Answer 30

ut's the same thing right? the 4/1*x/4 and canceling the 4s and being left with x?

Answer 31

pretty much since f(x) = g(x)

Answer 32

tHe_FiZiCx99 I typed in f^{-1}(x)

Answer 33

No, I meant how t\do you verbally say it ~ f of inverse x ~ ?

Answer 34

oh you say "f inverse"

Answer 35

Ohh, ty :>

Answer 36

you're welcome

Answer 37

Thank you sosososososososososo much!!!!

Answer 38

sure thing