Actually what you posted is the definition of an inverse function. To find an inverse you swap the positions of x and y and solve for y.

Ex) if f(x) = 6x+17

then to find write y=6x+17

swap x and y's placement x = 6y+17

solve for y,

and so

You can check that the second function, that may be referred to as g(x), is an inverse to f(x) by seeing that g(f(x))=f(g(x)).

Using the above example to see this (and calling [tex]f^{-1}(x) by the name g(x)):

and so g(x) is indeed the inverse function of f(x)

Now we can see that just to show the reverse that would follow your question better:

write

swap x and y placement

6x = y-17

6x+17 = y