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.
The Attempt at a Solution
Initially I did this, thinking the reflection shifts to the right:
g(x) = f(x + c)
f^-1(g(x)) = x + c
x = f^-1(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?