Question

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Answer 1

@Michele_Laino

Answer 2

Please note that:
\[f(g(x))=\frac{ g(x)-9 }{ g(x)+5 }\]
please continue

Answer 3

no, please note tath:
\[f(g(x))=\frac{ \frac{ -5x-9 }{ x-1 }-9 }{ \frac{ -5x-9 }{ x-1 }+5 }=...\]

Answer 4

oops...note that...

Answer 5

Ohh I get what i did wrong ok

Answer 6

So would top and bottom cancel out and leave us with f(g(x)) = -9 / 5?

Answer 7

no, you have to compute the sum at the numerator, and the sum at denominator, for example, what is:
\[\frac{ -5x-9 }{ x-1 }-9=...\]
and then compute this, please:
\[\frac{ -5x-9 }{ x-1 }+5=...\]

Answer 8

for the first one, we have:
\[\frac{ -5x-9-9(x-1) }{ x-1 }=...\]
please continue

Answer 9

for the second fraction you have to compute this:
\[\frac{ -5x-9+5(x-1) }{ x-1 }=...\]

Answer 10

I do not understand what to do next or how to compute them

Answer 11

for example:
first fraction:
\[=\frac{ -5x-9-9x+9 }{ x-1 }=\frac{ -9x }{ x-1 }\]
now, please do the same with the second fraction

Answer 12

5x / x -1?

Answer 13

no, before I have made an error, here is the right answer:
\[first \quad fraction=\frac{ -14x }{ x-1 }\]
second fraction:
\[=\frac{ -5x-9+5x-5 }{ x-1 }=\frac{ -14 }{ x-1 }\]

Answer 14

Now we have to return at our expression for f(g(x)), which is:
\[f(g(x))=\frac{ \frac{ -14x }{ x-1 } }{ \frac{ -14 }{ x-1 } }=...\]
please simplify

Answer 15

ok! that's right!, We ahve made the first part of your problem
since we have showed that f(g(x))=x.
Now you have to do a similar procedure in order to show that g(f(x))=x

Answer 16

please your starting point is:
\[g(f(x))=\frac{ -5f(x)-9 }{ f(x)-1 }=\frac{ -5\frac{ x-9 }{ x+5 }-9 }{ \frac{ x-9 }{ x+5 } -1}=...\]

Answer 17

I think that you have forgotten an "x"

Answer 18

for the top one

Answer 19

ok!
So what is your result?

Answer 20

ok! that's right!
You have showed that g(f(x))=x, so you have completed the answer to the second part of your exercise!

Answer 21

Thank you so much! Very helpful :)

Answer 22

Thank you! :)