Question

Diene claims that f(x)=3/x is its own undo rule. Is her conjecture correct?

Answer 1

An undo rule is the alias for the inverse of a function.

One of the definitions of an inverse f^-1(x) of a function f(x) is such that
f(f^(x))=x
The definition can be used to check if a function is the inverse of another, as illustrated in the following example.


Let f(x)=x+5
we have y=x+5
To find the inverse, we switch x and y and solve for y in terms of x.
So x=y+5 => y=x-5
So f^-1x = x-5
Check:
f(f^-1(x))
=f(x-5)
=(x-5) + 5
=x
So y=x-5 is the inverse of y=x+5.

Another example:
y=log(x), now switch x and y and solve for y
x=log(y)
exponentiate:
e^x = y
y=e^x is the inverse of y=log(x)
check
f(f^-1(x))
=log(e^x)
=x
So y=e^x is the inverse of y=log(x)

Try
y=3/x
and check if 3/x is the inverse of 3/x.