How do you verify if #f(x)=7x; g(x)=1/7x# are inverse functions?

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Answer 1 · 2017-04-14T22:33:52

See below.

We swap the places of #x# and #y# (in this case, #f(x)#).

#y=7x#

#x=7y#

#1/7x=y#, which is #g(x)#, so the functions are inverses of each other.

Answer 2 · 2017-04-15T15:51:14

Here's another way of going at it. Apply the identity #f(f^-1(x)) = x#.

#f(f^-1(x)) = f(g(x)) = 7(1/7x) = x color(green)(√)#

Check the other way:

#f^-1(f(x)) = g(f(x)) = 1/7(7x) = x color(green)(√)#

Hence, #f(x)# and #g(x)# are indeed inverses of each other.

Hopefully this helps!