As there isn't much to do to find it analytically, I suppose they mean guess at it?

Anyway, to find the inverse of a function f(x) use the following steps:

1) Set y = f(x)

2) Now let x = f(y) (This amounts to reflecting the graph over the line y = x, which graphically gives the inverse function.)

3) Solve for y. We'll have y = g(x) as the solution. g(x) is the inverse to f(x).

In this case:

1) Let y = f(x) = 7x

2) Let x = 7y

3) y = (1/7)x <-- This is the inverse function, .

To prove this we need to show that

So

(Check!)

(Check!)

-Dan