Calculus help please!!!

Determine whether f(x)= (x-b)/(a) is one to one; if it is find f inverse

Let y = f(x)= {(x-b)/(a)}------------------(1);
y1 = {(x1-b)/(a)} and
y2 = {(x2-b)/(a)} or
(y2 -y1) = [(x2-x1)/a] ------------- (2)
From (2) it follows y2-y1 ≠ 0 if x2-x1 ≠ 0
So f(x)= {(x-b)/(a)} is one to one function.
From (1) it follows
ay = x-b or
x = ay +b; exchanging x and y
f⁻¹(x) = ax +b

let y = f(x)

y = (x - b)/a
y = x/a - b/a

a and b constants, each value of x will give one value of y; this is a one to one

y = (x - b)/a
ay = x - b
x = ay + b

inverse function
f ⁻¹(x) = ax + b