Question

Find the inverse function of f(x)=(x+4)/(2x-5) and then verify your result using: f(f^-1(x))=x and f^-1(f(x))=x. Please an answer fast

Answer 1

swap variables and solve for y

x = (y+4)/(2y-5)
(2y-5)x = y+4
2xy-5x = y+4
(2x-1)y = 5x+4
f^-1 = y = (5x+4)/(2x-1)

I'll check one way, you can at least do the other.

If we let g f^-1, then
f(g) = (g+4)/(2g-5)
= ((5x+4)/(2x-1) + 4)/(2(5x+4)/(2x-1) - 5)
= ((13x)/(2x-1))/((13)/(2x-1))
= x