Find the inverse function of f1x for the following onetoone

Find the inverse function of f^-1(x), for the following one-to-one function: f(x) = 3x+2/2x-5

given f(x) = (3x+2) / (2x-5)

so let us say f(x) =y

then x = f^-1(y)

so we have to find the \'x\' value from f(x)

y = (3x+2) /(2x-5)

y(2x-5) =(3x+2)

2xy -5y = 3x+2

2xy -3x -5y-2=0

x(2y-3) = 5y+2

x = (5y+2) /(2y-3)

but x= f^-1(y) = (5y+2)/(2y-3)

f is one one function so plug x in theplace of y

so f ^-(x) = (5x+2)/(2x-3)

the inverse function is (5x+2)/(2x-3)