What is the inverse function of y equals 7x plus 2?

Answer 1

First, this function is strictly increasing on the entire real line, so an inverse exist on the entire real line.

We define inverse of function f, denoted f^-1 such that

if y = f(x) then f^-1(y) = x

Or to find the inverse, all is needed is to isolate x in terms of y.

In this case, y = 7x + 2

7x = y - 2

x = (y - 2)/7

So the inverse is x = (y - 2)/7

What? You don't like function in terms of y? Well, they are just meaningless variables anyway, you can write whatever, in particular

the inverse is y = (x - 2) / 7 (the x, y here are independent with the x, y above. If you are getting confused, write b = (a - 2)/7 where b is a function of a)