Inverse Linear Functions
If y = f(x) = a + bx , then it isn't difficult to solve for x and find an algebraic rule for x in terms of y :
x = f –1(y) = (y – a) / b
If we write this as f –1(y) = (1/b)y – (a/b) , we see that the inverse is just another linear function with slope 1/b and y-intercept –a/b .
Notice that the inverse is undefined whenever b = 0 . This is the case whenever the forward function, f , is constant, with a graph that's a horizontal line.