Question

How do you find the inverse of `f(x) = 4/x`?

Answer 1

The inverse is `x = 4/(f(x))` or `f(x) = 4/x`
(same as original)

Explanation:

To find the inverse, we swap the x and y values.

The original equation is `f(x) = 4/x`, meaning that the inverse would be `x = 4/(f(x))`.

If you want it with `f(x)` by itself, first multiply `f(x)` on both sides of the equation:
`x quadcolor(blue)(*quadf(x)) = 4/f(x) quadcolor(blue)(*quad(f(x))`

`x(f(x)) = 4`

Divide both sides by `color(blue)x`:
`(x(f(x)))/color(blue)x = 4/color(blue)x`

Therefore,
`f(x) = 4/x`

As you can see, the inverse is the same as the original equation. This can be proved by graphing both equations:
Graphing original `f(x) = 4/x`:

Graphing inverse `x = 4/f(x)`:

(desmos.com)

As you can see, both graphs are the same.

Hope this helps!