find and simplify

Question

Let r(x) = 2x-7/3x+4 find and simplify r-1(x)

Answer 1

 r( X ) = (2X - 7) / (3x +4 )  I think this is what you mean. Place your parenthesis properly.

 

    You have to solve X in therm of r(X).

 

   It is easy if you let: r(x) =y

    

       Y = (2x - 7 ) / ( 3X + 4 )

 

         Solve X in terms of Y :

         

            3XY + 4Y = 2X - 7 

 

            3X Y - 2X = -4Y - 7

      

            X  ( 3Y - 2 ) = - 4Y -7

 

             X = (-4y -7) /( 3Y - 2 )

 

               Substitute f^-1(X) , and X for Y

 

               f^-1( X ) = ( 4X + 7 ) / ( 2 - 3X)