The inverse of f(x)=4x is x/4.
Inverse of f(x) is written f-1(x). If f-1(f(x))=f(f-1(x))=x then f-1(x) is the true inverse.
Let's see what f-1(f(x)) is. Since f(x)=4x, then we can substitute for f(x):
f-1(f(x))=f-1(4x)=4x/4=x✔️
Let's see what f(f-1(x)) is. f-1(x)=x/4 so f(f-1(x))=f(x/4)=4(x/4)=x✔️
This proves that f-1(x)=x/4.
