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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).
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