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

1 Answer
Jan 11, 2017

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]}