Verified answer

y = [ -2 - 3x ] / [ 3 + 3 x] ----> y [ 3 + 3x ] = - 2 - 3x --->

x [ 3y + 3 ] = - 2 - 3y ---> x = [ - 2 - 3y ] / [ 3 + 3 y ]...

thus f is its own inverse

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

f is defined for

3+3x different from 0

that is 3x different from -3

that is x different from -1.

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

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

3yx+3y=-2-3x

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

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

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

f^-1=f

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

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

x( 3 + 3f^( - 1 ) (x ) ) = - 2 - 3 f^( - 1 ) (x )

3x + 3xf^( - 1 ) (x ) = - 2 - 3f^( - 1 ) ( x )

3x + 2 = - 3 f^( - 1 ) ( x ) - 3xf^( - 1 ) ( x )

3x + 2 = ( - 3 - 3x ) f^( -1 ) (x )

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