How do you show that #f(x)=(x+3)/(x-2)# and #g(x)=(2x+3)/(x-1)# are inverse functions algebraically and graphically?

1 Answer
Noah G
Jun 1, 2017

If #f(x)# is the initial function, and #f^-1(x)# is the inverse function, then

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

So here we go:

#f(g(x)) = ((2x + 3)/(x - 1) + 3)/((2x + 3)/(x - 1) - 2)#

#f(g(x))= ((2x + 3 + 3x - 3)/(x -1))/((2x +3 - 2x + 2)/(x- 1))#

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

#f(g(x)) = (5x)/5#

#f(g(x)) = x#

This proves that #f(x)# and #g(x)# are inverses.

Hopefully this helps!

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