How do you find the inverse of #f(x) =x/(x-1)#?

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Answer 1 · 2018-05-03T21:46:49

#y = xy - x#

To find the inverse of a function, we swap the #x# to a #y# and vice versa.

Therefore, the equation becomes:
#x = y/(y-1)#

Now, like the normal way to write equations, we want what #y# equals.

So Let's make #y# alone by multiplying both sides by #color(blue)(y-1)#:
#x quadcolor(blue)(*quad(y-1)) = y/(y-1) quadcolor(blue)(*quad(y-1))#

#x(y-1) = y#

Distribute:
#xy - x = y#

Write with #y# on the left hand side:
#y = xy - x#

Hope this helps!