What is the inverse function of #f(x) =1/x#?

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Answer 1 · 2018-06-11T23:05:26

#f^-1 = 1/x#

Given: #f(x) = 1/x#

To find the inverse function, first let #f(x) = y: " "y = 1/x#

Switch #x " and " y: " "x = 1/y#

Solve for #y#, by multiplying both sides by #y#:

#x * y = 1/cancel(y) *cancel(y)/1#

#xy = 1#

Divide both sides by #x: " "(cancel(x)y)/cancel(x) = 1/x#

#f^-1 = 1/x#