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

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Answer 1 · 2017-01-11T10:22:32

Please see below.

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]}