Question

Let f(x) = x+1/x+m. Find the inverse f^-1(x). For what value of m is f(x) = f^-1(x)?

Answer 1

To get f(x)^-1, flip the numerator and denominator around
f(x)^-1=(x+m)/(x+1)

Answer 2

i got y(x-1) = 1-xm is that right @M0j0jojo

Answer 3

?

Answer 4

To find the inverse of f(x)=y
you need to solve f(x)=y for x.

Answer 5

\[y=\frac{x+1}{x+m} \text{ solve for x}\]

Answer 6

I will help you out with the first couple of steps
...
Multiply (x+m) on both sides
(x+m)y=x+1
xy+my=x+1
xy-x=1-my

Answer 7

See if you can figure out what comes next...
Remember you are trying to solve for x.

Answer 8

Actually based on what you said you know the next step
x(y-1)=1-my

now divide both sides by (y-1)

Answer 9

\[x=\frac{1-my}{y-1} \\ f^{-1}(y)=\frac{1-my}{y-1} \\ \text{ So } f^{-1}(x)=\frac{1-mx}{x-1}\]

Answer 10

So you want to find m such that
\[\frac{1-mx}{x-1}=\frac{x+1}{x+m}\]

Answer 11

If you just compare the bottoms what do you think m needs to be?

Answer 12

is the answer -1?

Answer 13

yes if m=-1 on bottom we have x-1 on both bottom's
and we also see that works on top
because 1+x is x+1

Answer 14

ok thank you soooo much :)