Anyone know how to find the inverse of functions?

Question

dumbcow · Answer

yep...say you have function f(x) ...to get inverse basically solve for x in terms of f(x)
example:
y = 5x -2
get "x" by itself
x = (y+2)/5

so inverse or f^-1 = (x+2)/5

anonymous · Answer

the inverse of y= (2x-3)/y+1

anonymous · Answer

x= 2y-3/y+1, I'm stuck here...

anonymous · Answer

what was the original function?

anonymous · Answer

y=2x-3/x+1

dumbcow · Answer

first, get rid of fraction by multiplying both sides by (x+1)

$$(x+1)y = 2x-3$$
then distribute and get all "x's" to one side
$$xy + y = 2x-3$$
$$xy-2x = -y-3$$
factor out an x
$$x(y-2) = -y-3$$
divide
$$x = \frac{-y-3}{y-2} = \frac{-(y+3)}{y-2}$$

anonymous · Answer

Aghh,  my brain. I'll try to understand what you did. Thank you for your help. :]

dumbcow · Answer

haha ok

anonymous · Answer

I mean, I totally understand what you did... but it's just having to reapply the same concept to another problem is just... too out there, man. >__<

dumbcow · Answer

yeah it takes a little practice to see what to do...typically its all about finding a way to get all terms with "x" on 1 side so you can factor it out, then divide