Question

How to inverse this function: y = 1/(x - 1)?

I'm not sure quite how to continue past the point of this:

x = 1/(y - 1)

Trying to isolate the y, but what is the correct step to take after this?

Thanks.

Answers

You are correct so far. To isolate y, multiply both sides by y - 1 to get:

x(y - 1) = 1.

Then, expand the left side:

xy - x = 1.

Adding x to both sides:

xy = x + 1.

Then, dividing both sides by x isolates y:

y = (x + 1)/x.

Therefore, f^-1(x) = (x + 1)/x.

I hope this helps!

#1

y=1/(x-1)

y(x-1)=1

x.y-y=1

x.y=y+1

x=(y+1)/y

Ans:y=(x+1)/x

#2

With x= 1/(y-1)

Then x/1= 1/(y-1). Cross multiply

X(y-1)=1

xy-x=1

Xy=1+x

Y=(1+x)/x

Hoping this helps!

#3

Hi,

Step 1) x = 1/ (y-1)

Step 2) Reciprocal both sides (flip each side over)

1/x = y-1

Step 3) Put the -1 to the other side and isolate the y

y = 1/x + 1

Step 4) (Optional)

y = (1+x) /x

viola!

#4