C(n)=10n+20 what is the inverse function of n(c)

First to make things very simple intuitively, it should be clear what an inverse function is.  For every value (x,y) from f(x), the inverse function will produce (y,x).  So in essence an inverse function is the reversal of coordinates of all points produced by f(x).

So to find an inverse function for f(x) or y, you must solve for the independent variable x and then simply switch variable labels.  In this case:

c=10n+20  solve for n, first subtract 20 from both sides

c-20=10n  divide both sides by 10

(c-20)/10=n  now reverse variable labels...

c=(n-20)/10

So if

C(n)=10n+20

C^-1(n)=(n-20)/10