Answer: The inverse is x/5
===============================================
How I got this answer:
The original function has 5x or 5*x, which reads out "five times x"
We have some unknown number x and we are multiplying it by 5. The inverse function undoes everything the original f(x) function does. Since the opposite of multiplicaiton is division, this means our answer involves dividing by 5.
--------
Here is a more algebraic explanation
f(x) = 5x
y = 5x .... replace f(x) with y
x = 5y
5y = x
y = x/5 .... divide both sides by 5 (to undo the multiplication)
g(x) = x/5 .... replace y with g(x)
here g(x) represents the inverse of f(x)
One useful property of inverses is that f( g(x) ) = g( f(x) ) = x