Question

How do you find the inverse of `f(x)=4/x` and graph both f and `f^-1`?

Answer 1

Please see below.

Explanation:

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

then `xy=4` and `x=y/4`

Hence `f^(-1)(x)=4/x`

and graph of the two are same and `xy=4`,

some of the points on the graph are

`(8,1/2), (4,1), (2,2), (1,4), (1/2,8)` as also `(-8,-1/2), (-4,-1), (-2,-2), (-1,-4), (-1/2,-8)`

Further, as `x->+-oo`, `y->0` and as `y->+-oo`, `x->0`

and as such we have `x=0` and `y=0` as asymptotes

and the graph appears as follows:
graph{xy=4 [-10, 10, -5, 5]}