Functions question, please help (more inside)

It is given that f(x) = m + nx, where m and n are constants. Given also that f(0) = 1 and f(4) = 21, giving reasons, find the value of:
a) m,
b) n, and,
c) (f)^ -1 (21)

*You are not supposed to use a calculator for this question. Please explain your answers and show your working.

a. for any f(x) = m + nx, f(0) is equal to constant

Since f(0) = 1 it follows that m = 1

b. Since f(4) = 21, then 21 = 1 + n(4)

21 -1 = 4n

5 = n

c. The function f(x) = 5x + 1, its inverse is f^-1(x) = (x - 1)/5 and by replacing x by 21

f^-1(21) = (21 - 1)/5

f^-1(21) = 20/5 or 4

1st eqn (m= 1) , f(0) = 1 -> m+nx = 1 -> m= 1-n(0) -> m=1
2nd eqn (n=5) , f(4) = 21 -> m+nx=21 -> m+4n=21 -> 1+4n=21 -> 4n=20 -> n=5

forgot the c

here's the solution
let y = (f^-1)(x) -> y=1+5x -> (y-1)/5=x
therefore, (f^-1)(x) =(x-1)/5

(f^-1)(21) = (21-1)/5 = 4