Question

How do you find the inverse of `f(x) = 4/x` and is it a function?

Answer 1

The inverse is `x=4/y` which is a function.

Explanation:

First, let's assign a variable to the value of the function

`f(x)=y=4/x`

Now we solve for `x` in terms of `y`. Multiply both sides by `x` and divide both sides by `y` to get the inverse

`x=4/y`

For an equation to be a function, there must be a single value of `x` for each `y` in the range, which is the case. Interestingly, the inverse is the same as the original function! This particular function is called a rectangular hyperbola.