If we shift a curve to the left what happens to its reflecti

If we shift a curve to the left, what happens to its reflection about 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. (b) Find an expression for the inverse of h(x)=f(cx), where c?0. (Denote f?1(x) as k below).

(1 point) (a) If we shift a curve to the left, what happens to its reflection about the line y y? n view of this geometric principle, find an expression for the inverse of g(x) -f(x c), where f s a one-to-one function. (b Find an expression for the inverse of h(x) -f(cx, where c 0, (Denote as kl below). (a) g (x)

Solution

For some functions f(x). the reflection about y=x is the same as taking the inverse , x= f^-1(y)nad graphing this as a function of y.

so if we graph y=f^-1(x)we will have the reflection of f(x).

if y=f(x+c) then x=f^-1(y)-c

so the inverse of f(x+c) is the reflection about the line y=x+c

the inverse of f(x+c) is the function y=f^-1(x)+c