Question

Please help me with algebra 2

Answer 1

what is it?

Answer 2

Use composition of functions to determine if f(x) and g(x) are inverses.

\[f(x) = \frac{ 3-x }{?x }\]

\[g(x)=\frac{ 3 }{ x+1 }\]

Answer 3

oops

Answer 4

oops, ignore the question mark on the first function

Answer 5

find \( f(g(x)) \)

Answer 6

I know, but i'm not sure how to simplify f(g(x))

Answer 7

then if u see \( f(g(x)) = x \) so they are inverse.

Answer 8

if in fact they are inverses expect a whole orgy of cancellation leaving you with only \(x\)

Answer 9

ok,
\(\Large f(g(x)) = \frac{ 3-\frac{ 3 }{ x+1 } }{ x }\)

Answer 10

ok,what have u done so far?

Answer 11

I am having trouble simplifying, do I try to clear the fraction on the numerator???

Answer 12

sure

Answer 13

do that

Answer 14

get rid of the compound fraction by multiplying top and bottom by \(x+1\) would be my first choice
there are other ways

Answer 15

Sorry, i'm having trouble, if I multiply by x+1 how would the fractions clear?

Answer 16

Can someone please show the work???

Answer 17

\(\Large \frac{ 3-\frac{ 3 }{ x+1 } }{ x } = \frac{ \frac{ 3x+3-3}{ x+1 } }{ x } = \frac{ 3 }{ x+1 }\)

Answer 18

which means they are NOT inverses
maybe there was a typo somewheres

Answer 19

Wait, shouldn't the denominator be 3/x+1

Answer 20

yes it's 3\x+1

Answer 21

so they're not inverse...

Answer 22

No, you also have to plug in 3/x+1 to the denominator of f(x) i think

Answer 23

no ;) i first pluged in g(x) :\( \Large f(g(x)) = \frac{ 3-\frac{ 3 }{ x+1 } }{ x } \)

Answer 24

and found it that is equal to \( \Large \frac{ 3-\frac{ 3 }{ x+1 } }{ x } = \frac{ \frac{ 3x+3-3}{ x+1 } }{ x } = \frac{ 3 }{ x+1 } \)

Answer 25

got it? @science00000

Answer 26

I think you're wrong...

Answer 27

why did you just leave the x on the denominator when you have to plug in g(x)

Answer 28

\( \Large f(g(x)) = \frac{ 3-\frac{ 3 }{ x+1 } }{ x } \) did u get this that what i did?

Answer 29

why did you only plug in g(x) to the numerator

Answer 30

Oops ! specially thank u for ur awesome carefulness ;) yes

Answer 31

in that way we can write : \(\Large f(g(x)) = \frac{ \frac{ 3x }{ x+1 } }{ \frac{ 3 }{ x+1 } }\)

Answer 32

Steps:

1) replace f(x) with the variable y.
2) change all of the x's to y's and the y's to x's
3) solve for y

If the result is the other function, in this case g(x), then the function is an inverse.