Question regarding inverse functions

by michellemich
Tags: functions, inverse
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,361 Question regarding inverse functions If you want to know if this is true for all invertible functions, it is simple enough to find a counterexample. If, say, f(x)= 2x+ 3, then $f(x)= 3x- 2$, then $f^{-1}(x)= (x+ 2)/3$. f(x+3)= 3(x+ 3)- 2= 3x+ 7. The inverse of that function is $(x- 7)/3$. Is that equal to $f^{-1}(x+ 3)= (x+3+ 2)/3= (x+ 5)/3$?