Find the inverse function  f^-1 (x) if f(x) = (x+1)/(2x-5)?

1 Answer | Add Yours

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll interchange x and y and we'll have:

x =  (y+1)/(2y-5)

Now, we'll multiply both sides by 2y - 5:

x(2y - 5) = y + 1

We'll remove the brackets:

2xy - 5x = y + 1

We'll keep all the terms in y to the left side, the rest of term being shifted to the right side.

2xy - y = 5x + 1

We'll factorize by y to the left side:

y(2x - 1) =5x + 1

We'll divide by 2x - 1

y = (5x + 1)/(2x - 1)

The inverse function is: f^-1(x) = (5x + 1)/(2x - 1).

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question