Question

How do you find the inverse of `y = 3x-9` and is it a function?

Answer 1

`x=(y+8)/3`. In general, if y=f(x), a function of x, `f^(-1)(y)=x`.
The operators`f and f^(-1)` are each the inverse operator for the other.

Explanation:

Solving for x, `x=(y+8)/3`.
In inversions, y may be a single-valued function of x. But, inversely, x might be many-valued, and vice versa.

For example, `y =x^2 > 0`, is single, valued. Inversely, `x=+-sqrt y` has two values.

In the example, `y=sin^(-1)x` is many-valued. The inverse x = sin y is single-valued.