How do you find the inverse of #f(x) = \frac{1}{x-5}# algebraically?

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Answer 1 · 2014-10-24T02:58:36

Step 1:

#f(x)=1/(x-5)#

Change #f(x)# to #y#

#y=1/(x-5)#

Step 2:

Switch #x# and #y#

#x=1/(y-5)#

Step 3:

Solve for #y#

#x(y-5)=1#

#(x(y-5))/x=1/x#

#(y-5)=1/x#

#y=1/x+5#