Question

Will give medal!! please help :)

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

f(x)=(x-8)/(x+7)
g(x)= (-7x-8)/(x-1)

Answer 1

So f(g(x)) is basically placing the function g(x) into any variable x in f(x)
\[f(g(x))=\frac{(\frac{-7x-8}{x-1})-8}{(\frac{-7x-8}{x-1})+7}\]
Now solve and simplify and show that f(g(x)=x
Now we do the same thing for g(f(x))

Answer 2

\[g(f(x))=\frac{-7(\frac{x-8}{x+7})-8}{(\frac{x-8}{x+7})-1}\]
And now we simplify and show that g(f(x))=x

Answer 3

not seeing how that equals x

Answer 4

Well you need to simplify
What have you tried so far?

Answer 5

well the (x-8)/(x+7) is in the numerator and denominator so I cancelled those out

Answer 6

which legt -7(-8)/ -1

Answer 7

left*

Answer 8

\[(g(x))=\frac{(\frac{-7x-8}{x-1})-8}{(\frac{-7x-8}{x-1})+7}=\frac{(\frac{-7x-8}{x-1})-\frac{8(x-1)}{x-1}}{(\frac{-7x-8}{x-1})+\frac{7(x-1)}{x-1}}=\frac{(\frac{-7x-8-8x+8}{x-1})}{(\frac{-7x-8+7x-7}{x-1})}=\frac{\frac{-15x}{x-1}}{\frac{-15}{x-1}}=\frac{-15x}{-15}=x\]

Answer 9

Okk the last part unfortunately got cut off but here it is
\[=\frac{-15x}{-15}=x\]