if f(x)=(2x-1)/(x+2), find the inverse if possible

This is a little tricky !!!......we want to first get x by itself

y = (2x-1)/(x+2)   multiply   both sides by x +  2

y(x +2)  = 2x - 1

xy + 2y =  2x - 1

xy - 2x =  -2y - 1

x ( y - 2)  = -(2y + 1 )   divide  both sides by y - 2

x  =  -(2y + 1) / (y - 2)     .......now ...."swap"  x and y

y  = - (2x + 1) / ( x - 2)     and for y, write  f^-1 (x)

f^-1 (x )  =  - (2x + 1) / (x - 2)