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## Homework Statement

If we shift a curve to the left, what happens to its reflection in the line

*y*=

*x*? In view of this geometric principle, find an expression for the inverse of

*g*(

*x*) =

*f*(

*x*+

*c*) where

*f*is a one-to-one function.

## Homework Equations

## The Attempt at a Solution

Initially I did this, thinking the reflection shifts to the right:

*(*

g

g

*x*) =

*f*(

*x*+

*c*)

*f^*-1(

*g*(

*x*)) =

*x*+

*c*

x =f^-1(

x =

*g*(

*x*)) -

*c*

then

*g*-1(

*x*) =

*f*-1(

*g*(

*x*)) -

*c*

I soon realised that the reflection actually shifts downward and the correct answer is slightly different, with the above calculation being` unnecessary. What I would like to know is, where did the above method using the cancellation equations go wrong?