How do you find the inverse of #f(x) =1/x#?

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Answer 1 · 2015-09-19T02:56:28

#f^(-1)(x)=1/x#

#f(x) = 1/x=># write #x# as a function of #y:#

#y = 1/x=># switch #x and y:#

#x = 1/y=># solve for #y:#

#y=1/x=># this is the inverse function of #f(x):# hence

#f^(-1)(x)=1/x#

To check let#:f(x)=1/x , g(x)=1/x:#

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

hence #g# is the inverse of #f# and #f# is the inverse of #g.#