Question

Confirm that f and g are inverses; f(g(x)) & g(f(x))

Answer 1

f(x)=x-9/x+5 ; g(x)=-5x-9/x-1

Answer 2

can you rewrite that with parentheses so we know what is in the denominator and what is not?

Answer 3

if they are inverses f(g(x)) = x = g(f(x))

Answer 4

@Eleven17 Could you help with this?

Answer 5

I can help if you show me what you need:)
I don't know if that is x -(9/x) -5 or (x-9)/(x-5) or ((x-9)/x) - 1 ....

Answer 6

you need to use parentheses as you would with a calculator.

Answer 7

\[f(x)=(x-9)/(x+5) \]

\[g(x)=(-5x-9)/(x-1)\]

Answer 8

Does that help?

Answer 9

zzr0ck3r has it right, if f and g are inverses, than plugging one equation into the other should return the value of x
So you want to just plug in the whole equation for g, where ever there is an x in f

Answer 10

So do you just plug in the function where ever there is an x?

Answer 11

Yeah, but I suck at fractions, especially when fractions are IN fractions

Answer 12

Yes! Think of it like this \[f(x)=\sin(x) \]\[g(x)=\sin^{-1}(x)\]
\[f(g(x))=\sin(\sin^{-1}(x))=x\]
Sin and arcsin are obviously inverse functions!

Answer 13

f(g(x)) = ((-5x-9)/(x-1) - 9 ) / ( (-5x-9)/(x-1) + 5 )
= (-5x-9-9x+9)/(-5x-9+5x-5) = (-14x)/(-14) = x

Answer 14

So if i did it right then they are inverses..

Answer 15

g(f(x)) (-5(x-9)/(x+5) - 9)/((x-9)/(x+5) - 1) =
((-5x+45)/(x+5) - 9)/((x-9-x-5)/(x+5))
= (-5x+45-9x-45)/(x-9-x-5) = (-14x)/-14 = x

Answer 16

sorry I don't know that fancy latek stuff

Answer 17

Fine by me ^-^