How do you show that #f(x)=1/x# and #g(x)=1/x# are inverse functions algebraically and graphically?

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Answer 1 · 2018-02-17T21:35:36

See below.

If #f(x)# and #g(x)# are inverse functions, then:

#f(g(x))=g(f(x))=x#

#1/g(x)=1/f(x)=x#

#1/(1/x)=1/(1/x)=x#

#x=x=x#

Since these are there own inverses we would expect their graphs to be symmetrical about the line #y=x#

The graph below confirms this:

enter image source here