If f(x) = 2x-1 and g(x) = 1/x how do you determine x such that f(g(x)) = g(f(x))?

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Answer 1 · 2015-09-18T04:59:33

x=1

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

Now equate both #2/x -1= 1/(2x-1)#

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

#4x-2-2x^2 +x =x#

#2x^2 -4x+2=0#

# x^2 -2x +1=0#

#(x-1)^2=0#
x=1