Question

find (f o g)^-1 (x)

Answer 1

Assuming that f and g are inverse functions, then you will get x.

But you havent stated in the stem that they are inverses. If they arent inverses or you dont know they are inverses, then you cannot find a solution unless you know what f and g are.

Answer 2

\[f (x) = (x - 6)/x\]
\[g(x) = x+5\]

Answer 3

I know they are inverse functions and I tried to solve for them but I couldn't figure it out.

Answer 4

would you not put x+5 in for the other x in the denominator?

Answer 5

Sorry for the immense errors, I'm multi tasking.

\[f(g(x)) = \frac{x-1}{x+5} \]

Then find the inverse

Answer 6

I'm having problems finding the inverse. I keep getting stuck

Answer 7

You need my help? whats the question, if any?

Answer 8

I tried to find the inverse of this so I could find the inverse of the problem but I kept getting stuck f(g(x))=x−1/x+5

Answer 9

you want to find the inverse of
y = (x-1)/(x+5)

so now you want x as a function of y

y(x+5) = x-1
yx + 5y = x - 1
yx -x = -5y - 1
x(y-1) = -(5y+1)
x = (5y+1)/(1-y)

Answer 10

ok. Now do I find the inverse of g?

Answer 11

\(\bf f(x) = y = \cfrac{x-6}{x}\qquad \qquad g(x)= x+5\\ \quad \\
f(\quad g(x)\quad ) = h = \cfrac{(x+5)-6}{(x+5)}\qquad inverse \implies x = \cfrac{(h+5)-6}{(h+5)}\)

Answer 12

no. that is it.

Answer 13

we found the inverse of f o g and that is what we needed

Answer 14

oh wow that was much easier than I thought.