What is the range of the function #f(x) = 1 / (x-2)#?

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Answer 1 · 2017-05-14T08:45:03

The range of #f(x)# is #=RR-{0}#

The range of a function #f(x)# is the domain of the function #f^-1(x)#

Here,

#f(x)=1/(x-2)#

Let #y=1/(x-2)#

Interchanging #x# and #y#

#x=1/(y-2)#

Solving for #y#

#y-2=1/x#

#y=1/x-2=(1-2x)/x#

Therefore,

#f^-1(x)=(1-2x)/(x)#

The domain of #f^-1(x)# is #=RR-{0}#

Therefore,

The range of #f(x)# is #=RR-{0}#
graph{1/(x-2) [-12.66, 12.65, -6.33, 6.33]}