Show that the function f in A= R-{2/3} defined as f(x)=4x+3/6x-4 is one -one and onto. Hence find the inverse of f.

fx=4x+36x-4For One-One4x1+36x1-4=4x2+36x2-44x1+36x2-4=4x2+36x1-424x1x2-16x1+18x2-12=24x1x2-16x2+18x1-12-16x1+18x2=-16x2+18x1-34x1=-34x2x1=x2so, fx is one-oneFor ontoLet y=4x+36x-4y6x-4=4x+36xy - 4y =4x + 36xy -4x =3 +4yx6y-4=3+4yx=3+4y6y-4Now , f3+4y6y-4=43+4y6y-4+363+4y6y-4-4                             =12+16y+18y-1218+24y-24y+16=34y34=ySo, fx is Ontoand f-1x=3+4x6x-4

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